Zuazua, Enrique

Publications

2015

PUBLISHED (1)

• Lescarret V., Zuazua E. Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces Mathematics of Computation, Volume 84, Number 291, January 2015, Pages 119–152

To Appear (7)

• Ervedoza S., Marica A., Zuazua E. Numerical meshes ensuring uniform observability of 1d waves: construction and analysis IMA J. Numerical Anal.
• Casas E., Vexler B., Zuazua E. Sparse Initial Data Identification for Parabolic PDE and its Finite Element Approximations Mathematical Control and Related Fields
• Lecaros R., Zuazua E. Control of 2D scalar conservation laws in the presence of shocks Mathematics of Computation
• Marica A., Zuazua A. Propagation of 1-D Waves in Regular Discrete Heterogeneous Media: A wigner measure approach Journal of Foundations of Computational Mathematics. 2014, 10.1007/s10208-014-9232-x
• Privat Y., Trélat E., Zuazua E. Optimal shape and location of sensors or actuators in PDE models. 2014 American Control Conference, Portland, Oregon, USA
• Privat Y., Trélat E. and Zuazua E. Complexity and regularity of maximal energy domains for the wave equation with xed initial data Discrete and Continuous Dynamical Systems-Series A.
• Privat Y., Trélat E., and Zuazua E. Optimal observability of the multi-dimensional wave and Schrödinger equations in quantum ergodic domains Journal of European Math. Society

Submitted (15)

• Lohéac J., Zuazua E. From averaged to simultaneous controllability of parameter dependent finite-dimensional systems
• Gugat M., Trélat E., Zuazua E. Optimal Neumann control for the 1D wave equation: Finite horizon, infinite horizon, boundary tracking terms and the turnpike property
• LÜ Q., Zuazua E. On the lack of controllability of fractional in time ODE and PDE
• Lohéac, J., Zuazua E. Averaged controllability of parameter dependent wave equations
• Chaves-Silva F.W., Zhang X., Zuazua E. Controllability of evolution equations with memory
• Zuazua E. Robust observation of Partial Differential Equations by additive perturbations
• Porretta A., Zuazua E. Numerical Hypocoercivity for the Kolmogorov Equation
• Allahverdi A., Pozo A., Zuazua E. Numerical aspects of the sonic-boom control
• Lü Q., Zuazua E. Averaged controllability for Random Evolution Partial Differential Equations
• Privat Y., Trélat E., Zuazua E. Optimal location of sensors and actuators for wave and heat processes
• Allahverdi N., Pozo A., Zuazua E. Numerical aspects of large-time optimal control of burgers equation
• Porretta A., Zuazua E. Remarks on long time versus steady state optimal control
• Lecaros R., Zuazua E. Tracking control of 1D Scalar Conservation laws in the presence of shocks
• Beli, N., Ignat, L., Zuazua, E. Dispersion for 1-d Schrödinger and wave equations with bv coefficients
• Zuazua E. Numerics for the Control of Partial Differential Equations



2014

PUBLISHED (11)

• Privat Y., Trélat E., Zuazua E. Optimal shape and location of sensors for parabolic equations with random initial data Archives Rat. Mech. Anal. Digital Object Identifier (DOI) 10.1007/s00205-014-0823-0
• Trélat E., Zuazua E. The turnpike property in finite-dimensional nonlinear optimal control Journal of Differential Equations 218 (2015), 81-114
• Lazar M., Zuazua E. Averaged control and observation of parameter-depending wave equations C. R. acad. Sci. Paris, Ser. I 352 (2014) 497-502
• Zuazua E. Averaged Control Automatica, Automatica 50 (2014) 3077–3087, http://dx.doi.org/10.1016/j.automatica.2014.10.054.
• Ignat L.I., Pozo A., Zuazua E. Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws Mathematics of Computation. S0025-5718-2014-02915-3, December 11, 2014.
• Chaves-Silva F.W., Rosier L., Zuazua E. Null controllability of a system of viscoelasticity with a moving control. Journal de Mathématiques Pures et Appliquées 101 (2014) 198-222, doi: 10.1016/j.matpur.2013.05.009
• Marica A., Zuazua E. Boundary stabilization of numerical approximations of the 1-d variable coefficients wave equation: A numerical viscosity approach Optimization with PDE Constraints. ESF Networking Program 'OPTPDE', Lecture Notes in Computational Science and Engineering, Vol. 101, September 2014, Springer International Publishing, pp. 285-324, ISBN 978-3-319-08024-6, DOI 10.1007/978-3-319-08025-3_9.
• Privat, Y., Trélat, E., Zuazua, E. Optimal sensor location for wave and Schrödinger equations Proceedings of the Conference in Hyperbolic Problems: theory, Numerics and Applications, Padova, 2012, Fabio Ancona, Alberto Bressan, Pierangelo Marcati and Andrea Marson, eds., AIMS on Applied Mathematics, Vol. 8, American Institute of Mathematical Sciences (AIMS), pp. 89-107. ISBN-10: 1-60133-017-0; ISBN-13: 978-1-60133-017-8
• Nersisyan H., Dutykh D., Zuazua E. Generation of two-dimensional water waves by moving bottom disturbances IMA Journal of Applied Mathematics (2014), pp. 1-19. DOI:10.1093/imamat/hxu051
• Lu Q., Zuazua E. Robust null controllability for heat equations with unknown switching control mode Discrete and Continuous Dynamical Systems, 34 (10), (2014), 4183-4210,
• Marica A., Zuazua E. Symmetric discontinuous Galerkin approximations of waves: high frequency propagation and control Springer Briefs in Mathematics, 2014.



2013

PUBLISHED (12)

• Fanelli F., Zuazua E. Weak observability estimates for $1-D wave equations with rough coefficients Annales IHP, DOI: 10.1016/j.anihpc.2013.10.004.
• Ignat, L., Zuazua, E. Asymptotic expansions for anisotropic heat kernels J. Evol. Equs., 13 (1) (2013), 1-20.
• Porretta A., Zuazua E. Long time versus steady state optimal control SIAM J. CONTROL OPTIM., 51 (6) (2013), 4242–4273.
• Ersoy M., Feireisl E., Zuazua E. Sensitivity analysis of 1-d steady forced scalar conservation laws Journal of Differential Equations 254 (2013) 3817–3834
• Ervedoza S., Zuazua E. On the numerical approximation of exact controls for waves Springer Briefs in Mathematics, 2013, XVII, 122 p., ISBN 978-1-4614-5808-1.
• Privat Y., Trélat E., Zuazua E. On the best observation of wave and Schrodinger equations in quantum ergodic billiards Journées EDPs, (2012), Exposé n. X, 13 pp
• Cazenave T., Escobedo M., Zuazua E. Blow-up for a time-oscillating nonlinear heat equation Acta Math. Univ. Comenianae. (N.S.), Vol. LXXXII, 1 (2013), pp. 125–146.
• Privat Y., Trélat E., Zuazua E. Optimal location of controllers for the one-dimensional wave equation Annales de l'IHP. Analyse non Linéaire. DOI 10.1016/j.anihpc.2012.11.005 AIHP. AN 30 (2013) 1097–1126.
• Cazacu C., Zuazua E. Improved multipolar Hardy inequalities Progress in Nonlinear Differential Equations and Their Applications 84, M. Cicognani et al (eds.), pp. 39-57, © Springer Science+Business Media New York 2013. Studies in Phase Space Analysis with Applications to PDEs,
• Privat Y., Trélat E., Zuazua E. Optimal observation of the one-dimensional wave equation J. Fourier Anal. Appl. DOI 10.1007/s00041-013-9267-4 bf 19 (2013) no.3, 514-544
• Casas E., Zuazua E. Spike Controls for Elliptic and Parabolic PDE Systems and Control Letters, Systems and Control letters, 62 (2013), 311-318.
• Zuazua E. Control and stabilization of waves on 1-d networks Control and stabilization of waves on $1-d$ networks, in "Modelling and Optimisation of Flows on Networks", Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle, Series: Lecture Notes in Mathematics, Vol. 2062, Subseries: C.I.M.E. Foundation Subseries, Ambrosio, L., Bressan, A., Helbing, D., Klar, A., Zuazua, E., 2013.



2012

PUBLISHED (10)

• Palacios F., Duraisamy K., Alonso J. J., Zuazua E. Robust Grid Adaptation for Efficient Uncertainty Quantification AIAA Journal, 50 (7) (2012), 1538-1546.
• Wang G., Zuazua E. On the equivalence of minimal time and minimal norm controls for heat equations SIAM J. Cont. Optim., Vol. 50, No. 5, (2012) pp. 2938–2958
• Zuazua E. A remark on the observability of conservative linear systems ``Proceedings of Multi-scale and high-contract PDE: from modelling, to mathematical analysis, to inversion", Habib Ammari, Yves Capdeboscq, and Hyeonbae Kang, eds. Contemporary Mathematics, AMS, Vol. 577, 2012, pp. 47-59.
• Bueno-Orovio A., Castro C., Palacios F., Zuazua E. Continuous adjoint approach for the Spalart-Allmaras model in aerodynamic optimization AIAA Journal, Vol. 50, No. 3, (2012) 631-646, DOI: 10.2514/1.J051307
• Marica A., Zuazua E. On the quadratic finite element approximation of 1-d waves: propagation, observation and control SIAM J. Numer. Anal. Vol. 50, No. 5, pp. 2744–2777.
• Porretta A., Zuazua E. Null controllability of viscous Hamilton-Jacobi equations Annales IHP, Analyse non lin'eaire, 29 (2012), pp. 301-333.
• Marica A., Zuazua E. On the quadratic finite element approximation of 1-d waves: propagation, observation, control and numerical implementation "CFL-80: A Celebration of 80 Years of the Discovery of CFL Condition", C. Kubrusly and C. A. Moura, eds., Springer Proceedings in Mathematics, Springer Verlag, 2012, p. 75-100, ISBN-10: 0817683933
• Ervedoza S., Zuazua E. The Wave Equation: Control and Numerics ``Control and stabilization of PDE's", P. M. Cannarsa y J. M. Coron, eds., “Lecture Notes in Mathematics” 2048, CIME Subseries, Springer Verlag, 2012, pp. 245-340.
• Arrieta J.M., Lopez-Fernandez M., Zuazua E. Approximating travelling waves by equilibria of non local equations Asymptotic Analysis 78 (2012) 145–186
• Ignat L., Zuazua E. Convergence rates for dispersive approximation schemes to nonlinear Schrödinger equations Journal de Mathématiques Pures et Appliquées. 98 (2012) 479–517



2011

PUBLISHED (11)

• Micu S., Zuazua E. On the regularity of null-controls of the linear 1-d heat equation C. R. Acad. Sci. Paris, Ser. I 349 (2011) 673–677, doi : 10.1016/j.cr
• Arrieta J. M., Lopez-F. M., Zuazua E. On a nonlocal moving frame approximation of traveling waves C. R. Acad. Sci. Paris, Ser. I 349 (2011) 753–758, DOI: 10.1016/j.crma.2011.07.001
• Casado-Diaz J., Castro C., Luna-Laynez M., Zuazua E. Numerical approximation of a one-dimensional elliptic optimal design problem SIAM J. Multiscale Modeling & Simulation, vol 9, Issue: 3, Pages: 1181-1216
• Ervedoza S., Zuazua E. Observability of heat processes by transmutation without geometric restrictions Mathematical Control and Related Fields, Volume 1, Number 2, June 2011, pp. 177-187, doi:10.3934/mcrf.2011.1.177
• Ervedoza S., Zuazua E. Sharp observability estimates for heat equations Archive for Rational Mechanics and Analysis, Volume: 202, Issue: 3 Pages: 975-1017
• Marica A., Zuazua E. High frequency wave packets for the Schrodinger equation and its numerical approximations C. R. Acad. Sci. Paris, Ser. I 349 (2011) 105–110
• Krejcirik D., Zuazua E. The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide J. Differential Equations 250 (2011) 2334–2346
• Micu S., Zuazua E. Regularity issues for the null-controllability of the linear 1-d heat equation Systems and Control Letters, 60 (2011) 406-413
• Castro C., Zuazua E. Flux identification for 1-d scalar conservation laws in the presence of shocks Math. Comp. 80 (2011), no. 276, 2025–2070
• Zuazua E. Switching control J. Eur. Math. Soc. 13 (2011), 85-117
• Beauchard K., Zuazua E. Large time asymptotics for partially dissipative hyperbolic systems Arch. Rational Mech. Anal. 199 (2011), 177–227



2010

PUBLISHED (11)

• Araruna D., Braz e Silva P., Zuazua E. Asymptotics and stabilization for dynamic models of nonlinear beams Proceedings of the Estonian Academy of Sciences, 2010, 59, 2, 150?155
• Marica A., Zuazua E. Localized solutions and filtering mechanisms for the discontinuous Galerkin semi-discretizations of the 1-d wave equation C. R. Acad. Sci. Paris Ser. I, 348 (2010), 1087-1092.
• Marica A., Zuazua E. Localized solutions for the finite difference semi-discretization of the wave equation C. R. Acad. Sci. Paris Ser. I, 348 (2010), 647-652.
• Marica A., Zuazua E. Localized solutions for the finite difference semi-discretization of the wave equation PICOF'10 Proceedings, pp. 135-141.
• Araruna F. D., Braz e Silva P., Zuazua E. Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system J. Systems Science and Complexity, 23(3) (2010), 414-430.
• Ervedoza S., Zuazua E. A systematic method for building smooth controls for smooth data Discrete Contin. Dyn. Syst. Ser. B, 14 (4) (2010) 1375-1401
• Munch A., Zuazua E. Numerical approximation of null controls for the heat equation: Ill-posedness and remedies Inverse Problems 26(8) 085018 (2010) (39 pp.)
• Krejcirik D., Zuazua E. The Hardy inequality and the heat equation in twisted tubes J. Mathématiques Pures et Appliquées, 94 (2010) 277?303
• Zhang X., Zheng C., Zuazua E. Exact Controllability of the Time Discrete Wave Equation: a Multiplier Approach Applied and Numerical PDEs: Scientific Computing in Simulation, Optimization and Control and Its Multiphysics Applications", W. Fitzgibbon, Yu. Kuznetsov, P. Neittaanmaki, J. Periaux y O. Pironneau eds., ECCOMAS SPRINGER series, 15 (2010), 229-245.
• Castro C., Palacios F., Zuazua E. Optimal control and vanishing viscosity for the Burgers equation Integral Methods in Science and Engineering, Vol. 2. Computational Methods, Birkhauser-Boston, C. Constanda and M. E. P'erez eds., pp. 65-90, 2010.
• Valein J., Zuazua E. Stabilization of the wave equation on 1-d networks SIAM J. Cont. Optim., 48 (4) (2010), 2771-2797



2009

PUBLISHED (10)

• Castro C., Lozano C., Palacios F., Zuazua E. A systematic formulation of the continuous adjoint method applied to viscous aerodynamic design Investigación Oper. 30 (2009), no. 1, 3--10
• Ervedoza S., Zuazua E. Uniformly exponentially stable approximations for a class of damped systems J. Math. Pures Appl. (9) 91 (2009), no. 1, 20--48,
• Vancostenoble J., Zuazua E. Hardy Inequalities, Observability, and Control for the Wave and Schrödinger Equations with Singular Potentials SIAM J. Math. Anal. Volume 41, Issue 4, pp. 1508-1532 (2009)
• Ervedoza S., Zuazua E. Uniform exponential decay for viscous damped systems ``Phase Space Analysis of PDEs 2007", Progress in Nonlinear Differential Equations and Their Applications, Birh"auser, Antonio Bove, Daniele Del Santo and M.K. Venkatesha Murthy eds., Volume 78, pp. 95-112.
• Zhang X., Zheng C., Zuazua E. Time discrete wave equations: Boundary observability and control Discrete and Continuous Dynamical Systems, Volume: 23, Number: 1/2, January/February 2009, pp. 571?604.
• Ignat L., Zuazua E. Convergence of a two-grid algorithm for the control of the wave equation J. Eur. Math. Soc. (JEMS) 11 (2009), no. 2, 351--391,
• Ignat L., Zuazua E. Numerical dispersive schemes for the Nonlinear Schrödinger equation SIAM. J. Numer. Anal., Vol 47, issue 2, pp. 1366-1390 (2009).
• Teresa L., Zuazua E. Identification of the class of initial data for the insensitizing control of the heat equation Communications in Pure and Applied analysis, 8 (1) (2009),  457-471
• Beauchard K., Zuazua E. Some controllability results for the 2D Kolmogorov equation Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, 1793--1815
• Baeza T., Castro C., Palacios F., Zuazua E. 2D Euler shape design on non-regular flows using adjoint Rankine-Hugoniot relations AIAA Journal, {bf 47}, (3) (Mar. 2009), pp. 552-562.



2008

PUBLISHED (7)

• Zhang X., Zuazua E. On the optimality of the observability inequalities for Kirchhoff plate systems with potentials in unbounded domains Actas del "Eleventh International Conference on Hyperbolic Problems: Theory, Numerics and Applications", Lyon, Julio, 2006, "Hyperbolic Problems: Theory, Numerics, and Applications", S. Benzoni-Gavage and D. Serre, eds., Springer.
• Vancostenoble J., Zuazua E. Null controllability of heat equations with singular inverse-square potentials J. Funct. Anal. 254 (2008), no. 7, 1864--1902.
• Castro C., Palacios F., Zuazua E. An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks Mathematical Models and Methods in Applied Sciences Vol. 18, No. 3 (2008) 369?416
• Ervedoza S., Zheng C., Zuazua E. On the observability of time-discrete conservative linear systems J. Functional Analysis, 254 (12) 3037-3078.
• Ervedoza S., Zuazua E. Perfectly Matched Layers in 1-d: Energy decay for continuous and semi-discrete waves Numerische Mathematik, Numer. Math., 109:597?634
• Duyckaerts T., Zhang X., Zuazua E. On the optimality of the observability inequalities for parabolic and hyperbolic systems with potentials Annales de l'IHP: Analyse Nonlinéaire, 25, 141.
• Araruna F., Zuazua E. Controllability of the Kirchhoff System for Beams as Limit of the Mindlin-Timoshenko One SIAM J. Cont. Optim., Vol. 47, No. 4, pp. 1909?1938



2007

PUBLISHED (6)

• Zhang X., Zuazua E. Long time behavior of a coupled heat-wave system arising in fluid-structure interaction Archive for Rational Mechanics and Analysis 2007, vol. 184, no1, pp. 49-120
• Castro C., Zuazua E. Addendum to "Concentration and Lack of Observability of Waves in Highly Heterogeneous Media" Archive for Rational Mechanics and Analysis
• Castro C., Lozano C., Palacios F., Zuazua E. Control of Euler and Navier-Stokes Equations: Applications to Optimal Shape Design in Aeronautics Proceedings de la 9th European Control Conference (ECC'07)
• Castro C., Lozano C., Palacios F., Zuazua E. Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids AIAA Journal Vol. 45, No. 9, pp. 2125-2139
• Roder L., Tcheugoué Tébou, Zuazua E. Uniform boundary stabilization of the finite difference space discretization of the 1-d wave equation Advances in Computational Mathematics (2007) 26: 337?365
• Zuazua E. On the numerical approximation of the Helmholtz Equation at large wave numbers Matemática Contemporánea, special volume in honour of L. A. Medeiros, 32 (2007), 253-286.



2006

PUBLISHED (12)

• Zhang X., Zuazua E. A sharp observability inequality for Kirchhoff plate systems with potentials Computational and Applied Mathematics, Vol. 25 No. 2-3, pp 353-373, 2006.
• Micu S., Zuazua E. On the controllability of a fractional order parabolic equation SIAM J. Cont. Optim., 44 (6) (2006) 1950-197.
• Orive R., Zuazua E. Long-time behavior of solutions to a non-linear hyperbolic relaxation system J. Differential Equations, 228 (2006) 17-38.
• Cea M., Zuazua E. Finite Element Approximation of 2D Parabolic Optimal Design Problems Numerical mathematics and Advanced Applications, ENUMATH 2005, A. Bermúdez de Castro et al., eds, Springer, 2006, pp. 151-176.
• Ignat L., Zuazua E. Dispersive Properties of Numerical Schemes for Nonlinear Schrödinger Equations Foundations of Computational Mathematics, Santander, London Mathematical Society lecture Notes, 331, L. M. Pardo et al. eds, Cambridge University Press, pp. 181-207.
• Vázquez J.L., Zuazua E. Lack of collision in a simplified 1-dimensional model for fluid-solid interaction Mathematical Models and Methods in Applied Sciences, M3AS, 16 (5), 637-678.
• Koch H., Zuazua E. A hybrid system of PDE's arising in multi-structure interaction: coupling of wave equations in n and n − 1 space dimensions in "Recent trends in Partial Differential Equations", UIMP-RSME Santaló Sumer School, July 12-16, 204, AMS-RSME, J. L. Vázquez et al. eds, Mathematics 409, AMS, 2006, pp. 55-77.
• Zuazua E. Control and numerical approximation of the wave and heat equations Proceedings of the ICM 2006, Vol. III,"Invited Lectures", European Mathematical Society Publishing Hause, M. Sanz-Solé et. al. eds.
• Zuazua E. Controllability and Observability of Partial Differential Equations: Some results and open problems In Handbook of Differential Equations:Evolutionary Differential Equations, vol 3, C. M. Dafermos and E. Feireisl eds., Elsevier Science, pp. 527-621.
• Chenais D., Zuazua E. Finite Element Approximation of 2D Elliptic Optimal Design JMPA, 85
• Castro C., Lozano C., Palacios F., Zuazua E. A Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids AIAA-2006-0051, 44th Aerospace Sciences Meeting & Exhibit
• Zhang X., Zuazua E. Asymptotic Behavior of a Hyperbolic-parabolic Coupled System Arising in Fluid-structure Interaction International Series of Numerical Mathematics, Vol. 154, 445?455



2005

PUBLISHED (9)

• Fu X., Zhang X., Zuazua E. On the optimality of some observability inequalities for plate systems with potentials Proceedings of the Conference "Phase Space analysis and PDE", Pienza, November 2005, F. Colombini ed., Birkhäuser, pp. 117-132
• Micu S., Zuazua E. On the controllability of a fractional order parabolic equation Multiscale Model. Simul. 4 (2005), 1, 36--87 (electronic).
• Orive R., Zuazua E. Finite difference approximation of homogenization problems for elliptic equations Multiscale Model. Simul. 4 (2005), 1, 36--87 (electronic).
• Ignat L., Zuazua E. A two-grid approximation scheme for nonlinear Schrödinger equations: Dispersive properties and convergence C. R. Math. Acad. Sci. Paris 341 (2005), 6, 381-386.
• Ignat L., Zuazua E. Dispersive properties of a viscous numerical scheme for the Schrödinger equation C. R. Acad. Sci. Paris, Ser. I 340 (2005) 529?534.
• J. Rauch, X. Zhang Polynomial decay for a hyperbolic-parabolic coupled system J. Math. Pures Appl. (9) 84 (2005), 4, 407-470.
• Zuazua E. Propagation, Observation, Control and Numerical Approximation of Waves approximated by finite difference method SIAM Review
• Castro C., Zuazua E. Unique continuation and control for the heat equation from an oscillating lower dimensional manifold SIAM J. Control Optim
• Munnier A., Zuazua E. Large time behaviour for a simplified N-dimensional model of fluid-solid interaction Comm. PDE,Comm. Partial Differential Equations



2004

PUBLISHED (6)

• Zhang X., Zuazua E. Polynomial decay and control of a 1-d hyperbolic-parabolic coupled system J. Differential Equations 204 (2004), 2, 380-438.
• Micu S., Zuazua E. An Introduction to the Controllability of Partial Differential Equations in ``Quelques questions de théorie du contròle". Sari, T., ed., Collection Travaux en Cours Hermann, (2004), pp. 69-157.
• Negreanu M., Zuazua E. Discrete Ingham inequalities and applications C.R.Acad. Sci. Paris, Série I, 338, (2004), 4, 281-286.
• Negreanu M., Zuazua E. Convergence of a multigrid method for the controllability of a 1-d wave equation C.R.Acad. Sci. Paris, Série I, 338, (2004), 5, 413-418.
• Zuazua E. Optimal and Approximate Control of Finite-Difference Approximation Schemes for the 1-D Wave Equation Rendiconti di Matematica, Serie VIII, 24, (2004), 2, 201-237.
• Chenais D., Zuazua E. Approximation par éléments finis de problèmes elliptiques d'optimisation de forme singulière C.R.Acad. Sci. Paris, 338, (2004), 729-734.



2003

PUBLISHED (12)

• Zuazua E. Remarks on the controllability of the Schr"odinger equation. Quantum Control: mathematical and numerical challenges, CRM Proc. Lect. Notes Ser., {bf 33}, AMS Publications, Providence, R.I., 2003, pp. 181-199.
• Zhang X., Zuazua E. Unique continuation for the linearized Benjamin-Bona-Mahony equation with space-dependent potential Mathematische Annalen, 325, (2003), 543-582.
• Zhang X., Zuazua E. Polynomial decay and control of a 1-d model for fluid-structure interaction C.R. Acad. Sci. Paris, Serie I, 336, (2003), 745-750.
• Zhang X., Zuazua E. Control, observation and polynomial decay for a coupled heat-wave system C. R. Acad. Sci. Paris, Serie I, 336, (2003), 823-828.
• Negreanu M., Zuazua E. Uniform boundary controllability of a discrete 1-D wave equation Systems and Control Letters, 48, (2003), 3-4, 261-280.
• Tcheugoué Tébou L.R., Zuazua E. Uniform exponential long time decay for the space semi-discretizations of a damped wave equation with artificial numerical viscosity Numerische Mathematic, 95, (2003), 3, p. 563-598.
• Vázquez J.L., Zuazua E. Large time behavior for a simplified 1-d model of fluid-solid interaction Comunications in Partial Differential Equations, 28, (2003), 9-10, 1705-1738.
• Perla Menzala G., Zuazua E. The Energy Decay Rate for the Modified Von Kármán System of Thermoelastic Plates: An Improvement Applied Mathematics Letters, 16, (2003),531-534.
• Chenais D., Zuazua E. Controllability of an Elliptic equation and its Finite Difference Approximation by the Shape of the Domain Numerische Mathematik, 95, (2003), 63-99.
• Castro C., Zuazua E. Concentration and lack of observability of waves in highly heterogeneous media Arch. Rat. Mech. Ana. 164, (2003), 1, 39-72.
• Dehman B., Lebeau G., Zuazua E. Stabilization and Control for the Subcritical Semilinear Wave Equation Annales Ecole Normale Superieure de Paris, 36, (2003), 4, 525-551.
• Doubova A., Fernández-Cara E., González-Burgos M., Zuazua E. On the controllability of parabolic systems with a nonlinear term involving the state and the gradient SIAM Jouernal Control and Optimization, 41, (2003), 3, 798-819.



2002

PUBLISHED (11)

• Prado R., Zuazua E. Asymptotic Expansion for the Generalized Benjamin-Bona-Mahony-Burger Equation Differential and Integral Equations, 15, (2002), 12, 1409-1434.
• Dáger R., Zuazua E. Spectral boundary controllability of networks of strings C. R. Acad. Sci. Paris 334 (2002), 1-6.
• León L., Zuazua E. Boundary controllability of the finite-difference space semi-discretizations of the beam equation ESAIM:COCV, Un número especial en memoria de J. L. Lions, Tomo 2, (2002), 827-862.
• Vázquez J.L., Zuazua E. Complexity of large time behaviour of evolution equations with bounded data Chinese Annals of Mathematics, 23, ser. B (2002), 2, 293-310. Special issue in honor of J.L. Lions.
• Menzala G.P., Zuazua E. On a one-dimensional version of the dynamical Marguerre-Vlasov system Bulletin of the Brazilian Society of Mathematics 32, (2002), 3, 1-17.
• Zuazua E. Log-Lipschitz regulatity and uniqueness of the flow for a field in (W_loc^{n/p+1,p}(R^n))^n C.R. Acad. Sci. Paris, 335, (2002), 17-22.
• Zuazua E. Controllability of partial differential equations and its semi-discrete approximations Discrete and Continuous Dynamical Systems, 8, (2002), 2, 469-513.
• Fernández-Cara E., Zuazua E. Control for weakly blowing up semilinear heat equations "Nonlinear PDE's in condensed matter and reactive flows", Kluwer Academic Publishers, H. Berestycki and Y. Pomeau, eds., Kluwer Academic Publishers, (2002), 127-148.
• Fernández-Cara E., Zuazua E. On the null controllability of the one-dimensional heat equation with BV coefficients Computational and Applied Mathematics, 2, (2002), 1, 167-190.
• Castro C., Zuazua E. Localization of waves in 1-d highly heterogeneous media Archive Rational Mechanics and Analysis, 164, (2003), 1, 39-72.
• Lopez A., Zuazua E. Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density Annales IHP. Analyse non linéaire, 19, (2002), 5, 543-580.



2001

PUBLISHED (12)

• Orive R., Pazoto A., Zuazua E. Asimptotic expansion of damped wave equations with periodic coefficients Math. Models & Methods Appl. Sciences, 11 (7) (2001), 1285-1310
• Dáger R., Zuazua E. Controllability of star-shaped networks of strings C. R. Acad. Sci. Paris 332 (2001), 7, 621-626
• Liu W.J., Zuazua E. Uniform stabilization of the higher dimensional system of thermoelasticity with a nonlinear boundary feedback Quarterly Appl. Math. 59 (2001), 2, 269-314.
• Cabanillas V., Menezes S., Zuazua E. Null controllability in unbounded domains for the semilinear heat equation with nonlinearities involving gradient terms J. Optim. Theory Applications 110 (2001), 2, 245-264.
• Micu S., Zuazua E. On the lack of null controllability of the heat equation on the half-space Portugaliae Mathematica 58 (2001), 1, 1-24.
• Dáger R., Zuazua E. Controllability of tree-shaped networks of vibrating strings C. R. Acad. Sci. Paris 332 (2001), 12, 1087-1092.
• Ortega J., Zuazua E. On a Constrained Approximate Controllability Problem for the Heat Equation Journal Of Optimization Theory and Applications, 108, (2001), 1, 29-64.
• Ortega J., Zuazua E. Generic simplicity of the eigenvalues of the stokes system in two space dimensions Advances in Differential Equations. 6, (2001), 8, 987-1023.
• Ortega J., Zuazua E. Generic simplicity of the spectrum and stabilization for a plate equation SIAM J. Cont. Optim. 39 (2001), 5, 1585-1614.
• Zuazua E. Null control of a 1-d model of mixed hyperbolic-parabolic type "Optimal Control and Partial Differential Equations", J. L. Menaldi et al., eds., IOS Press, (2001), 198-210.
• Zuazua E. Some results and open problems on the controllability of linear and semilinear heat equation Vol. "Carleman estimates and applications to uniqueness and control theory", Cortona, F. Colombini and Z. Zuily, eds. Progr. Nonlinear Differential Equations Appls., 41, Birkhauser, Boston, pp. 193-213, (2001).
• Rodríguez-Bernal A., Zuazua E. Parabolic singular limit of a wave equation with localized interior damping Commun. Contemp. Math. 3, (2001), 2, 215-257.



2000

PUBLISHED (11)

• S. Micu On the lack of null controllability of the heat equation on the half-line Transactions of the A.M.S. 353 (2000), 4, 1635-1659.
• Teresa L., Zuazua E. Null controllability of linear and semilinear heat equations in thin domains Asymptotic Analysis, 24 (2000), 295-317.
• Ortega J., Zuazua E. Large time behavior in RN for linear parabolic equations with periodic coefficients Asymptotic Analysis 22 (2000), 1, 51-85.
• Vázquez J. L., Zuazua E. The Hardy inequality and the asymptotic behavior of the heat equation with an inverse square potential J. Funct. Anal. 173 (2000), 103-153.
• Menzala G. P., Zuazua E. Timoshenko's beam equation as a limit of a nonlinear one-dimensional von Kármán system Proc. Royal Soc. Edinburgh 130A (2000), 855-875.
• Fernández-Cara E., Zuazua E. The cost of approximate controllability for heat equations: The linear case Advances in Differential Equations 5 (2000), 4-6, 465-514.
• Fernández-Cara E., Zuazua E. Null and approximate controllability for weakly blowing up semilinear heat equations Annales de l'IHP. Analyse non linéaire 17 (2000), 5, 583-616.
• Castro C., Zuazua E. High frequency asymptotic analysis of a string with rapidly oscillating density Eur. J. Appl. Math. 11 (2000), 6, 595-622.
• Castro C., Zuazua E. Exact boundary controllability of two Euler-Bernouilli beams connected by a point mass Mathematical and Computer Modelling 32 (2000), 955-969.
• Castro C., Zuazua E. Low frequency asymptotic analysis of a string with rapidly oscillating density SIAM J. Appl. Math. 60 (2000), 1205-1233.
• López A., Zhang X., Zuazua E. Null controllability of the heat equation as a singular limit of the exact controllability of dissipative wave equations J. Math. Pures et Appl. 79 (2000), 741-809.



1999

PUBLISHED (9)

• Liu W-J., Zuazua E. Decay rates for dissipative wave equations, Ricerche di Matematica, XLVIII (1999), 61-75.
• Teresa L., Zuazua E. Approximate controllability of a semilinear heat equation in unbounded domains Nonlinear Analysis Theory, Methods Applications, 37 (1999), 1059-1090.
• Infante J. A., Zuazua E. Boundary observability for the space-discretizations of the one-dimensional wave equation M2AN 33 (1999), 2, 407-438.
• Sweers G., Zuazua E. On the non-existence of some special eigenfunctions for the Dirichlet Laplacian and the Lamé system J. Elasticity 52 (1999), 111-120.
• Leugering G., Zuazua E. On exact controllability of generic trees Actas del Congreso: "Contrôle de systèmes gouvernés par des équations aux dérivées partielles", Nancy, Francia, Marzo 1999, ESAIM Proceedings, vol. 8, F. Conrad y M. Tucsnak eds, pp. 95-105.
• Lebeau G., Zuazua E. Decay rates for the three-dimensional linear system of thermoelasticity Archives Rat. Mech. Anal. 148, (1999), 179-231.
• Zuazua E. Observability of 1-d Waves in Heterogeneous and Semi-Discrete Media "Advances in Structural Control", J. Rodellar et al. eds, CIMNE, Barcelona, (1999), 1-30.
• Zuazua E. Boundary observability for the finite-difference space semi-discretizations of the 2-d wave equation in the square J. Math. pures et appl., 78 (1999), 523-563.
• Zuazua E. Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities Control and Cybernetics, 28, (1999), 3, 665-683.



1998

PUBLISHED (7)

• Micu S., Zuazua E. Asymptotics for the spectrum of a fluid/structure hybrid system arising in the control of noise SIAM J. Math. Anal., 29, (1998), 4,967-1001
• Infante J.A., Zuazua E. Boundary observability for the space-discretizations of the 1-d wave equation C. R. Acad. Sci. Paris 326 (1998), 6, 713-718.
• Lebeau G., Zuazua E. Null Controllability of a System of Linear Thermoelasticity Archives for Rational Mechanics and Analysis. 141, (1998), 4, 297-329
• Perla Menzala G., Zuazua E. Energy decay of magnetoelastic waves in a bounded conductive medium Asymptotic Analysis, 18 (1998), 349-362
• Castro C., Zuazua E. Controllability of a hybrid system consisting of two flexible beams connected by a point mass SIAM J. Cont. Optim. 36 (1998), 5, 1576-1595
• López A., Zuazua E. Some new results related to the null controllability of the 1-d heat equation Seminario EDP de la Escuela Politécnica de Paris, VIII, 1-22
• Zuazua E. Some Problems and Results on the controllability of Partial Differential Equations Actas del Congreso: Second European Congress of Mathematics, Budapest, Julio 1996. Progress in Mathematics, vol. 169, 1998, Birkhäuser Verlag Basel/Switzerland, 276-311



1997

PUBLISHED (4)

• Micu S., Zuazua E. Boundary controllability of a linear hybrid system arising in the control of noise SIAM J. Cont. Optim. 35 (1997), no. 5, 1614-1638.
• Perla Menzala G., Zuazua E. Explicit Exponential Decay Rates for Solutions of von Kármán's System of Thermoelastic Plates C. R. Acad. Sci. París, 324, 1997, 49-54.
• Zuazua E. Decay rates in thermoelasticity Actas del Congreso: "International Conference on Shells", M. Bernadou, Ph. Ciarlet y J. Viaño eds., Ediciones de la Universidad de Santiago de Compostela, 1997, pp. 171-174.
• Castro C., Zuazua E. A hybrid system consisting of two flexible beams connected by a point mass: spectral analysis and well-possedness in asymmetric spaces En Elasticiti, Viscoelasticiti et Contrel Optimal, Aspects Theoriques et Numeriques, J. Blum and A. Raoult eds. ESAIM Proceedings, Vol.2, 17-53, (1997).



1996

PUBLISHED (6)

• Micu S., Zuazua E. On a weakly damped system arising in the control of noise International Series of Numerical Mathematics, Vol 126, Birkhäuser Verlag, (1996), 207-222.
• Micu S., Zuazua E. Stabilization and Periodic Solutions of a Hybrid System Arising in the Control of Noise Partial Differential Equations and Applications, Proceeding of the IFIP TC7/WG-7.2. 174, Dekker, New York, (1996), 219-230.
• Figueiredo I., Zuazua E. Exact Controllability and Asymptotic Limit for Thin Plates Asimptotic. Anal., 12 (1996) 213-252.
• Freitas P., Zuazua P. Stability results for the wave equation with indefinite damping J. Diff. Equations., 132, 2, (1996), 338-352.
• Teresa L., Zuazua E. Controllability of the linear system of thermoelastic plates Advances in Differential Equations, 1, 3, (1996), 369-402.
• Castro C., Zuazua E. Une remarque sur l'analyse asymptotique spectrale en homogénéisation C. R. Acad. Sci. Paris, 322, (1996), 1043-1047.



1995

PUBLISHED (3)

• Fabre C., Puel J. P., Zuazua E. Approximate controllability for the semilinear heat equation Proc. Roy. Soc. Edinburgh, 125A (1995), 31-61.
• Zuazua E. Controllability of the linear system of thermoelasticity Journal de mathématiques pures et apliquées, 74 (1995), 303-346.
• Rodríguez-Bernal A. Parabolic singular limit of a wave equation with localized boundary damping Discrete and Continuous Dynamical System, 1, 3, (1995), 303-346.



1994

PUBLISHED (1)

• Cox S., Zuazua E. The rate at which energy decays in a damped string Comm. P.D.E. (1 & 2), (1994), 213-243.



1993

PUBLISHED (1)

• Zuazua E. Exact Controllability for semilinear wave equations in one space dimension Annales de IHP, section C, 10 (1993) 109-129



1992

PUBLISHED (1)

• Zuazua E. A Dynamical System Approach to the Self-Similar Large Time Behavior in Scalar Convection-Diffusion Equations Journal of Differential Equations 108 1-35, (1992).



1991

PUBLISHED (2)

• Zuazua E. Exact boundary controllability for the semilinear wave equation Nonlinear Partial Differential Equations and their Applications, Ed. por H. Brezis y J. L. Lions, Coll\`ege de France Seminar 1987/1988. Vol. X, Research Notes in Mathematics, Pitman, 357-391 1991.
• Zuazua, E. Exponential decay for the semilinear wave equation with localized damping in unbounded domains J. Math. pures et appl. 70. 1991. 513-529



1990

PUBLISHED (2)

• Komornik, V., Zuazua, E. A direct method for the boundary stabilization of the wave equation J. Math. pures et appl. 69 (1). 33-55. 1990
• Zuazua, E. Exponential decay for the semilinear wave equation with locally distributed damping Comunn. in Partial differential Equations, 15 (2) 205-235



1988

PUBLISHED (1)

• Haraux, A., Zuazua, E. Decay estimates for some semilinear damped hyperbolic problems Archive for Rational Mechanics and Analysis. 100 (2). 191-206. 1988.



1987

PUBLISHED (1)

• Zuazua E., Lions J.L. . Contrôlabilité exacte d'un modèle de plaques vibrantes en un temps arbitrairement petit C. R. Acad. Se. Paris, t. 304, Série I, n° 7