Juan Luis Vázquez. Publications 2000-2018

The list of links to the pdf versions of the publications is still incomplete. We apologize for the inconvenience.
 
2000
  A125 Quenching for a one-dimensional fully nonlinear parabolic equation in detonation theory (authors: Victor A. Galaktionov, Stéphane Gerbi, J. L. V.), SIAM J. Appl. Math. 61 (2000/01), no. 4, 1253–1285.     pdf
  A126 Behaviour of interfaces in a diffusion-absorption equation with critical exponents (authors: Victor A. Galaktionov, Sergei I. Shmarev, J. L. V.), Interfaces Free Bound. 2 (2000), no. 4, 425–448.     pdf
  A127 The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential (authors: J. L. V., Enrike Zuazua), J. Funct. Anal. 173 (2000), no. 1, 103–153.     pdf
  A128 Asymptotics of the fast-diffusion equation with critical exponent (authors: Victor A. Galaktionov, Lambertus A. Peletier, J. L. V.), SIAM J. Math. Anal. 31 (2000), no. 5, 1157–1174.     pdf
  A129 Very intense pulse in the ground­wa­ter flow in fissurized porous stratum (authors: Grigori I. Barenblatt, E. A. Ingerman, H. Shvetz, J. L. V.), Proc. Natl. Acad. Sci. USA 97 (2000), no. 4, pp. 1366-1369.     pdf
 
2001
  A130 Uniqueness of solution to a free boundary problem from combustion (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Trans. Amer. Math. Soc. 353 (2001), no. 2, 655–692.     pdf
  A131 Asymptotic convergence of the Stefan problem to Hele-Shaw (authors: Fernando Quirós, J. L. V.), Trans. Amer. Math. Soc. 353 (2001), no. 2, 609–634.     pdf
  A132 Solutions of nonlinear parabolic equations without growth restrictions on the data. (authors: Lucio Boccardo, Thierry Gallouët,, J. L. V.), Electron. J. Differential Equations 2001, No. 60, 20 pp.     pdf
  A133 Extinction behaviour for fast diffusion equations with absorption (authors: Raúl Ferreira, J. L. V.), Nonlinear Anal. 43 (2001), no. 8, Ser. A: Theory Methods, 943–985.     pdf
  A134 Uniqueness in a two-phase free-boundary problem (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Adv. Differential Equations 6 (2001), no. 12, 1409–1442.     pdf
  A135 A mixed semilinear parabolic problem in a noncylindrical space-time domain. (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Differential Integral Equations 14 (2001), no. 4, 385–404.     pdf
 
2002
  A136 Theory of extended solutions for fast-diffusion equations in optimal classes of data. Radiation from singularities (authors: Emmanuel Chasseigne, J. L. V.), Arch. Ration. Mech. Anal. 164 (2002), no. 2, 133–187.     pdf
  A137 Complete blow-up and thermal avalanche for heat equations with nonlinear boundary conditions (authors: Quirós, Fernando; Rossi, Julio D.; J. L. V.), Comm. Partial Differential Equations 27 (2002), no. 1-2, 395–424.     pdf
  A138 Sets of admissible initial data for porous-medium equations with absorption (authors: Emmanuel Chasseigne, J. L. V.), Proceedings of the 2001 Luminy Conference on Quasilinear Elliptic and Parabolic Equations and System, 53–83, Electron. J. Differ. Equ. Conf., 8 , Southwest Texas State Univ., San Marcos, TX, 2002.     pdf
  A139 Obstructions to existence in fast-diffusion equations (authors: Ana Rodríguez, J. L. V.), J. Differential Equations 184 (2002), no. 2, 348–385.     pdf
  A140 Complexity of large time behaviour of evolution equations with bounded data (authors: J. L. V., Enrike Zuazua), Dedicated to the memory of Jacques-Louis Lions. Chinese Ann. Math. Ser. B 23 (2002), no. 2, 293–310.     pdf
  A141 Uniqueness of asymptotic profiles for an extinction problem (authors: Ferreira, R.; Galaktionov, V. A., J. L. V.), Nonlinear Anal. 50 (2002), no. 4, Ser. A: Theory Methods, 495–507.     pdf
  A142 The problem of blow-up in nonlinear parabolic equations (authors: Galaktionov, Victor A.; J. L. V.), Current developments in partial differential equations (Temuco, 1999). Discrete Contin. Dyn. Syst. 8 (2002), no. 2, 399–433.     pdf
  A143 Ignition and propagation in an integro-differential model for spherical flames (authors: Roquejoffre, Jean-Michel, J. L. V.), Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 3, 379–387     pdf
 
2003
  A144 Asymptotic behaviour for the porous medium equation posed in the whole space (author: J. L. V.), Dedicated to Philippe Bénilan. J. Evol. Equ. 3 (2003), no. 1, 67–118.     pdf
  A145 The pressure equation in the fast diffusion range (authors: Emmanuel Chasseigne, J. L. V.), Rev. Mat. Iberoamericana 19 (2003), no. 3, 873–917.     pdf
  A146 Introduction. Dedicated to Philippe Bénilan (authors: Haïm Brézis, Wolfgang Arendt, Louise Barthélemy, Michael Crandall, Jose Carrillo, J. Ildefonso Diaz, Jerome A. Goldstein, Michel Pierre, J. L. V.), J. Evol. Equ. 3 (2003), no. 1, 1–9.     pdf
  A147 The nonlinearly damped oscillator (author: J. L. V.), ESAIM Control Optim. Calc. Var. 9 (2003), 231–246.     pdf
  A148 Darcy's law and the theory of shrinking solutions of fast diffusion equations (author: J. L. V.), SIAM J. Math. Anal. 35 (2003), no. 4, 1005–1028.     pdf
  A149 Geometrical properties of solutions of the porous medium equation for large times (authors: Ki-Ahm Lee, J. L. V.), Indiana Univ. Math. J. 52 (2003), no. 4, 991–1016.     pdf
  A150 Fine asymptotics for fast diffusion equations (authors: José A. Carrillo, J. L. V.), Comm. Partial Differential Equations 28 (2003), no. 5-6, 1023–1056.     pdf
  A151 Intermediate asymptotics for a nonhomogeneous nonlinear heat equation (authors: V. A. Galaktionov, Sh. Kamin, R. Kershner, Kh. L. Vaskez, J. L. V.), (Russian) Tr. Semin. im. I. G. Petrovskogo No. 23 (2003), 61-92, 409; translation in J. Math. Sci. (N. Y.) 120 (2004), no. 3, 1277–1294.     pdf
  A152 Mathematics, science and technology: a deep and enduring connection (author: J. L. V.), (Portuguese) Bol. Soc. Port. Mat. No. 49 (2003), 19–70.     pdf
  A153 Large time behavior for a simplified 1D model of fluid-solid interaction (authors: J. L. V., Enrique Zuazua), Comm. Partial Differential Equations 28 (2003), no. 9-10, 1705–1738.     pdf
  A154 Study of self-similarity for the fast-diffusion equation (authors: Raúl Ferreira, J. L. V.), Adv. Differential Equations 8 (2003), no. 9, 1125–1152.     pdf
 
2004
  A155 The Dirichlet problem for the porous medium equation in bounded domains. Asymptotic behavior (authors: J. L. V.), Monatsh. Math. 142 (2004), no. 1-2, 81–111.     pdf
  A156 Thermal avalanche for blowup solutions of semilinear heat equations (authors: Quirós, Fernando; Rossi, Julio D.;, J. L. V.), Comm. Pure Appl. Math. 57 (2004), no. 1, 59–98.     pdf
  A157 Nonlinear diffusion and image contour enhancement (authors: G. I. Barenblatt, J. L. V.), Interfaces Free Bound. 6 (2004), no. 1, 31–54.     pdf
  A158 Intermediate asymptotics for a nonhomogeneous nonlinear heat equation (authors: V. A. Galaktionov, Sh. Kamin, R. Kershner, Vaskez, Kh. L= J. L. V.), (Russian) Tr. Semin. im. I. G. Petrovskogo No. 23 (2003), 61--92, 409; translation in J. Math. Sci. (N. Y.) 120 (2004), no. 3, 1277–1294.     pdf
  A159 Complexity of large time behaviour of evolution equations with bounded data (authors: J. L. V., Enrike Zuazua), "Frontiers in mathematical analysis and numerical methods", 267–295, World Sci. Publ., River Edge, NJ, 2004.     pdf
 
2005
  A160 Symmetrization and mass comparison for degenerate nonlinear parabolic and related elliptic equations. (author: J. L. V.), Adv. Nonlinear Stud. 5 (2005), no. 1, 87–131.     pdf
  A161 Failure of the strong maximum principle in nonlinear diffusion. Existence of needles. (author: J. L. V.), Comm. Partial Differential Equations 30 (2005), no. 7-9, 1263–1303.     pdf
  A162 The porous medium equation. New contractivity results (author: J. L. V.), in "Elliptic and parabolic problems", 433–451, Progr. Nonlinear Differential Equations Appl., 63, Birkhäuser, Basel, 2005.     pdf
  A163 Blow-up. El problema matemático de explosión para ecuaciones y sistemas de reacción-difusión (Mathematical blowup for reaction-diffusion equations and systems) (authors: de Pablo, A.; Ferreira, R.; Quirós, F. , J. L. V.), (Spanish) Bol. Soc. Esp. Mat. Apl. Se⃗MA No. 32 (2005), 75–111.     pdf
  A164 Viscosity solutions for quasilinear degenerate parabolic equations of porous medium type (authors: Brändle, Cristina , J. L. V.), Indiana Univ. Math. J. 54 (2005), no. 3, 817–860.     pdf
  A165 Singular free boundary problem from image processing (authors: A. L. Amadori, , J. L. V.), Math. Models Methods Appl. Sci. 15 (2005), no. 5, 689–715.     pdf
  A166 The diffusive limit for Carleman-type kinetic models (authors: Francesco Salvarani, J. L. V.), Nonlinearity 18 (2005), no. 3, 1223–1248.     pdf
 
2006
  A167 Large-time geometric properties of solutions of the evolution p-Laplacian equation (authors: Ki-ahm Lee, Arshak Petrosyan, J. L. V.), J. Differential Equations 229 (2006), no. 2, 389–411.     pdf
  A168 Global positivity estimates and Harnack inequalities for the fast diffusion equation (authors: Matteo Bonforte, J. L. V.), J. Funct. Anal. 240 (2006), no. 2, 399–428.     pdf
  A169 Classification of blow-up with nonlinear diffusion and localized reaction (authors: Raúl Ferreira, Arturo de Pablo, J. L. V.), J. Differential Equations 231 (2006), no. 1, 195–211.     pdf
  A170 A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media (authors: Guillermo Reyes, J. L. V.), J. Eur. Math. Soc. (JEMS) 8 (2006), no. 3, 531–554.     pdf
  A171 The Cauchy problem for the inhomogeneous porous medium equation (authors: Guillermo Reyes, J. L. V.), Netw. Heterog. Media 1 (2006), no. 2, 337–351.     pdf
  A172 Extended solutions for general fast diffusion equations with optimal measure data (authors: Emmanuel Chasseigne, J. L. V.), Adv. Differential Equations 11 (2006), no. 6, 627–646.     pdf
  A173 Lack of collision in a simplified 1D model for fluid-solid interaction (authors: J. L. V., Enrique Zuazua), Math. Models Methods Appl. Sci. 16 (2006), no. 5, 637–678.     pdf
  A174 Dirichlet boundary conditions can prevent blow-up reaction-diffusion equations and systems (authors: Marek Fila, Hirokazu Ninomiya, J. L. V.), Discrete Contin. Dyn. Syst. 14 (2006), no. 1, 63–74.     pdf
  A175 Stabilization towards a singular steady state with gradient blow-up for a diffusion-convection problem. (authors: Philippe Souplet, J. L. V.), Discrete Contin. Dyn. Syst. 14 (2006), no. 1, 221–234.     pdf
 
2007
  A176 Perspectives in nonlinear diffusion: between analysis, physics and geometry (author: J. L. V.), International Congress of Mathematicians. Vol. I, 609–634, Eur. Math. Soc., Zürich, 2007. ICM2006 Plenary speaker.     pdf
  A177 Multiple blowup for nonlinear heat equations at different places and different times (authors: Noriko Mizoguchi, J. L. V.), Indiana Univ. Math. J. 56 (2007), no. 6, 2859–2886.     pdf
  A178 Porous medium flow in a tube. Traveling waves and KPP behavior (author: J. L. V.), Commun. Contemp. Math. 9 (2007), no. 5, 731–751.     pdf
  A179 Localized non-diffusive asymptotic patterns for nonlinear parabolic equations with gradient absorption (authors: Philippe Laurençot. J. L. V.), J. Dynam. Differential Equations 19 (2007), no. 4, 985–1005.     pdf
  A180 Viscosity solutions for elliptic-parabolic problems (authors: Paola Mannucci, J. L. V.), NoDEA Nonlinear Differential Equations Appl. 14 (2007), no. 1-2, 75–90.     pdf
  A181 Asymptotic complexity in filtration equations (authors: José A. Carrillo, J. L. V.), J. Evol. Equ. 7 (2007), no. 3, 471–495.     pdf
  A182 Asymptotic behaviour of the porous media equation in domains with holes (authors: Cristina Brändle, Fernando Quirós, J. L. V.), Interfaces Free Bound. 9 (2007), no. 2, 211–232.     pdf
  A183 Finite-time blow-down in the evolution of point masses by planar logarithmic diffusion (authors: J. L. V.), Discrete Contin. Dyn. Syst. 19 (2007), no. 1, 1–35     pdf
  A184 Heat equation with dynamical boundary conditions of locally reactive type (authors: J. L. V., Enzo Vitillaro), Semigroup Forum 74 (2007), no. 1, 1–40.     pdf
  A185 Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations (authors: Matteo Bonforte, J. L. V.), Bound. Value Probl. 2007, Art. ID 21425, 31 pp.     pdf
  A186 Some new kernel functions for real-valued data (authors: J. L. V., Lluis Belanche, Miguel Vázquez), International Journal of Computer, Mathematical Sciences and Applications (Int. J. Comput. Math. Sci. Appl.), Vol. 1, no. 2 (2007), 149-160.     pdf
  A187 Hardy-Poincaré inequalities and applications to nonlinear diffusions (authors: Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, J. L. V.), C. R. Math. Acad. Sci. Paris 344 (2007) , no. 7, 431–436.     pdf
 
2008
  A188 Parabolic approach to Nonlinear Elliptic Eigenvalue Problems (authors: Ki-ahm Lee, J. L. V.), Advances in Mathematics, 219 (2008), 2006-2028.     pdf
  A189 Radial equivalence for the two basic nonlinear degenerate diffusion equations (authors: Razvan Iagar, Ariel Sánchez, J. L. V.), J. Math. Pures Appl. (9) 89 (2008), no. 1, 1-24.     pdf
  A190 Fast Diffusion Flow on Manifolds of Nonpositive Curvature (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), J. Evol. Equ. 8 (2008), no. 1, 99-128.     pdf
  A191 Heat equation with dynamical boundary conditions of reactive type (authors: J. L. V., Enzo Vitillaro), Comm. Partial Differential Equations 33 4 (2008), no. 4-6, 561-612.     pdf
  A192 Wave equation with second-order non-standard dynamical boundary conditions (authors: J. L. V., Enzo Vitillaro), Math. Models Methods Appl. Sci. (M3AS) 18 (2008), no. 12, 2019-205.     pdf
  A193 The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions (authors: Guillermo Reyes, J. L. V.), Commun. Pure Appl. Anal. 7 (2008), no. 6, 1275-1294.     pdf
  A194 Distance-Based Kernels for Real-Valued Data (authors: Lluís Belanche, J. L. V., Miguel Vázquez), in "Data Analysis, Machine Learning and Applications", pp. 3-10, Springer Berlin Heidelberg, 2008. ISBN 978-3-540-78246-9 (Online).     pdf
 
2009
  A195 Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds (authors: Peng Lu, Lei Ni, J. L. V., Cédric Villani), J. Math. Pures Appl. 91 (2009), no. 1, 1-19.     pdf
  A196 Asymptotics of the fast diffusion equation via entropy estimates (authors: Adrien Blanchet, Matteo Bonforte, Jean Dolbeault, Gabriele Grillo, J. L. V.), Arch. Rational Mech. Anal. 191 (2009), no. 2, 347-385.     pdf
  A197 Long time behavior for the inhomogeneous PME in a medium with slowly decaying density (authors: Guillermo Reyes, J. L. V.), Commun. Pure Appl. Anal. 8 (2009), no. 2, 493-508.     pdf
  A198 Measure-valued solutions and the phenomenon of blow-down in logarithmic diffusion (author: J. L. V.), J. Math. Anal. Appl. 352 (2009), no 1, 515-547.     pdf
  A199 Noncoercive convection-diffusion elliptic problems with Neumann boundary conditions (authors: Jérôme Droniou, J. L. V.), Cal. Var. Partial Differential Equations 34, Issue 4 (2009), 413-434.     pdf
  A200 Asymptotic analysis for the p-Laplacian Evolution Equation in an Exterior Domain (authors: Razvan G. Iagar, J. L. V.), Ann. Inst. H. Poincaré, Anal. Non Linéaire 26 (2009), no. 2, 497-520.     pdf
  A201 On the Laplace equation with dynamical boundary conditions of reactive-diffusive type (authors: J. L. V., Enzo Vitillaro), JMAA 354 (2009), no 2, 674-688.     pdf
 
2010
  A202 Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities (authors: Matteo Bonforte, J. Dolbeault, G. Grillo, J. L. V.), Proc. Natl. Acad. Sci. USA 107 (2010), no. 38, 16459–16464.     pdf
  A203 Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation (authors: Matteo Bonforte, Razvan G. Iagar, J. L. V.), Adv. Math. 224 (2010), no. 5, 2151–2215.     pdf
  A204 Special fast diffusion with slow asymptotics: entropy method and flow on a Riemann manifold (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Arch. Ration. Mech. Anal. 196 (2010), no. 2, 631–680.     pdf
  A205 Anomalous large-time behaviour of the p-Laplacian flow in an exterior domain in low dimension (authors: Razvan G. Iagar, J. L. V.), J. Eur. Math. Soc. (JEMS) 12 (2010), no. 1, 249–277.     pdf
  A206 Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations (authors: Matteo Bonforte, J. L. V.), Adv. Math. 223 (2010), no. 2, 529–578.     pdf
  A207 Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density (authors: Shoshana Kamin, Guillermo Reyes, J. L. V.), Discrete Contin. Dyn. Syst. 26 (2010), no. 2, 521–549.     pdf
 
2011
  A208 Nonlinear porous medium flow with fractional potential pressure (authors: Luis A. Caffarelli, J. L. V.), Arch. Ration. Mech. Anal. 202 (2011), no. 2, 537–565.     pdf
  A209 Asymptotic behaviour of a porous medium equation with fractional diffusion (authors: Luis A. Caffarelli, J. L. V.), Discrete Contin. Dyn. Syst. 29 (2011), no. 4, 1393–1404.     pdf
  A210 A fractional porous medium equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), Adv. Math. 226 (2011), no. 2, 1378–1409.     pdf
  A211 Highly time-oscillating solutions for very fast diffusion equations (authors: J. L. V., Winkler, Michael), J. Evol. Equ. 11 (2011), no. 3, 725–742.     pdf
  A212 The evolution of singularities in fast diffusion equations: infinite-time blow-down (authors: J. L. V., Winkler, Michael), SIAM J. Math. Anal. 43 (2011), no. 4, 1499–1535.     pdf
  A213 Multiple blow-up for a porous medium equation with reaction (authors: Noriko Mizoguchi, Fernando Quirós, J. L. V.), Math. Ann. 350 (2011), no. 4, 801–827.     pdf
  A214 Asymptotic behaviour of a nonlinear parabolic equation with gradient absorption and critical exponent (authors: Razvan G. Iagar, Philippe Laurençot, J. L. V.), Interfaces Free Bound. 13 (2011), no. 2, 271–295.     pdf
  A215 A continuum of extinction rates for the fast diffusion equation (authors: Marek Fila, J. L. V., , Michael Winkler ), Commun. Pure Appl. Anal. 10 (2011), no. 4, 1129–1147.     pdf
  A216 Heat equation with dynamical boundary conditions of reactive-diffusive type (authors: J. L. V., Enzo Vitillaro ), J. Differential Equations 250 (2011), no. 4, 2143–2161.     pdf
 
2012
  A217 A general fractional porous medium equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), Comm. Pure Appl. Math. 65 (2012), no. 9, 1242–1284.     pdf
  A218 Nonlinear diffusion with fractional Laplacian operators (author: J. L. V.), "Nonlinear partial differential equations", 271–298, Abel Symp., 7, Springer, Heidelberg, 2012.     pdf
  A219 Quantitative local bounds for subcritical semilinear elliptic equations (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Milan J. Math. 80 (2012), no. 1, 65–118.     pdf
  A220 Functional aspects of the Hardy inequality: appearance of a hidden energy (authors: J. L. V., Nikolaos B. Zographopoulos), J. Evol. Equ. 12 (2012), no. 3, 713–739.     pdf
  A221 A porous medium equation involving the infinity-Laplacian. Viscosity solutions and asymptotic behavior (authors: Manuel Portilheiro, J. L. V.), Comm. Pure Appl. Math. 65 (2012), no. 9, 1242–1284.     pdf
  A222 Rate of convergence to Barenblatt profiles for the fast diffusion equation (authors: Marek Fila, J. L. V., Michael Winkler, Eiji Yanagida), Arch. Ration. Mech. Anal. 204 (2012), no. 2, 599–625.     pdf
  A223 Large-time geometrical properties of solutions of the Barenblatt equation of elasto-plastic filtration (authors: Yong Huang, J. L. V.), Differential Equations 252 (2012), no. 7, 4229–4242.     pdf
  A224 Behaviour near extinction for the Fast Diffusion Equation on bounded domains (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), J. Math. Pures Appl. (9) 97 (2012), no. 1, 1–38.     pdf
 
2013
  A225 Regularity of solutions of the fractional porous medium flow (authors: Luis Caffarelli, Fernando Soria, J. L. V.), J. Eur. Math. Soc. (JEMS) 15 (2013), no. 5, 1701–1746.     pdf
  A226 Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space (authors: Matteo Bonforte, Filippo Gazzola, Gabriele Grillo, J. L. V.), Calc. Var. Partial Differential Equations 46 (2013), no. 1-2, 375–401.     pdf
  A227 Hardy type inequalities and hidden energies (authors: J. L. V., Nikolaos B. Zographopoulos), Discrete Contin. Dyn. Syst. 33 (2013), no. 11-12, 5457–5491.     pdf
  A228 Functional aspects of the Hardy inequality: appearance of a hidden energy (authors: J. L. V., Nikolaos B. Zographopoulos), Differential and difference equations with applications, 653–665, Springer Proc. Math. Stat., 47, Springer, New York, 2013.     pdf
  A229 Quantitative bounds for subcritical semilinear elliptic equations (authors: Matteo Bonforte, Gabriele Grillo, J. L. V.), Recent trends in nonlinear partial differential equations. II. Stationary problems, 63–89, Contemp. Math., 595, Amer. Math. Soc., Providence, RI, 2013.     pdf
  A230 Degenerate homogeneous parabolic equations associated with the infinity-Laplacian (authors: Manuel Portilheiro, J. L. V.), Calc. Var. Partial Differential Equations 46 (2013), no. 3-4, 705–724.     pdf
  A231 Asymptotic behaviour of the doubly nonlinear diffusion equation utpum on bounded domains (authors: Diana Stan, J. L. V.), Nonlinear Anal. 77 (2013), 1–32.     pdf
 
2014
  A232 Classical solutions for a logarithmic fractional diffusion equation (authors: Arturo de Pablo, Fernando Quirós, Ana Rodríguez, J. L. V.), J. Math. Pures Appl. (9) 101 (2014), no. 6, 901–924.     pdf
  A233 Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type (authors: J. L. V., Bruno Volzone), J. Math. Pures Appl. (9) 101 (2014), no. 5, 553–582.     pdf
  A234 Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type (author: J. L. V.), J. Eur. Math. Soc. (JEMS) 16 (2014), no. 4, 769–803.     pdf
  A235 A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators (authors: Sylvia Serfaty, J. L. V.), Calc. Var. Partial Differential Equations 49 (2014), no. 3-4, 1091–1120.     pdf
  A236 Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators (author: J. L. V.), Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no. 4, 857–885.     pdf
  A237 The Hele-Shaw asymptotics for mechanical models of tumor growth (authors: Benoît Perthame, Fernando Quirós, J. L. V.), Arch. Ration. Mech. Anal. 212 (2014), no. 1, 93–127.     pdf
  A238 Quantitative local and global a priori estimates for fractional nonlinear diffusion equations (authors: Matteo Bonforte, J. L. V.), Adv. Math. 250 (2014), 242–284.     pdf
  A239 The Fisher-KPP equation with nonlinear fractional diffusion (authors: Diana Stan, J. L. V.), SIAM J. Math. Anal. 46 (2014), no. 5, 3241–3276.     pdf
  A240 Finite and infinite speed of propagation for porous medium equations with fractional pressure (authors: Diana Stan, Félix del Teso, J. L. V.), C. R. Math. Acad. Sci. Paris 352 (2014), no. 2, 123–128.     pdf
  A241 The Maximum Principle (author: J. L. V.), In "Selected Papers of James Serrin", 2 volumes"(P. Pucci, V. Radulescu, H. Weinberger, Editors). Contemporary Mathematicians, Birkhäuser. Springer Basel, 2014.     pdf
  A242 Progress in the theory of Nonlinear Diffusion. Asymptotics via entropy methods (author: J. L. V.), "Trends in Contemporary Mathematics", V. Ancona & E. Strickland eds, Springer INdAM Series vol. 8, Springer, 2014.     pdf
 
2015
  A243 Fundamental solution and long time behavior of the porous medium equation in hyperbolic space (author: J. L. V.), J. Math. Pures Appl. (9) 104 (2015), no. 3, 454–484.     pdf
  A244 The mesa problem for the fractional porous medium equation (author: J. L. V.), Interfaces Free Bound. 17 (2015), no. 2, 261–286.     pdf
  A245 Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains (authors: Matteo Bonforte, Yannick Sire, J. L. V.), Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 5725–5767.     pdf
  A246 A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains (authors: Matteo Bonforte, J. L. V.), Arch. Ration. Mech. Anal. 218 (2015), no. 1, 317–362.     pdf
  A247 Transformations of self-similar solutions for porous medium equations of fractional type (authors: Diana Stan, Félix del Teso, J. L. V.), Nonlinear Anal. 119 (2015), 62–73.     pdf
  A248 Optimal estimates for fractional fast diffusion equations (authors: J. L. V., Bruno Volzone), J. Math. Pures Appl. (9) 103 (2015), no. 2, 535–556.     pdf
  A249 Free Boundary Problems: The Forefront of Current and Future Developments (authors: Gui-Qiang Chen, Henrik Shahgholian, J. L. V.), Phil. Trans. R. Soc. A 373 (2015), 20140285. 8 pages.     pdf
  A250 Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure (authors: José Antonio Carrillo, Yanhong Huang, M. C. Santos, J. L. V.), J. Differential Equations 258 (2015), no. 3, 736–763.     pdf
  A251 Some Free Boundary Problems involving Nonlocal Diffusion and Aggregation (authors: José Antonio Carrillo, J. L. V.), Phil. Trans. R. Soc. A 373 (2015), Issue 2050 , 20140275, 16 pp.     pdf
  A252 Regularity of solutions of the fractional porous medium flow with exponent 1/2 (authors: Luis Caffarelli, J. L. V.), Algebra i Analiz 27 (2015), no 3 [St. Petersburg Math. Journal 27 (2016), no 3, 437-460] (volume in honor of Prof. Nina Uraltseva).     pdf
 
2016
  A253 The Dirichlet problem for the fractional p-Laplacian evolution equation (author: J. L. V.), J. Differential Equations 260 (2016), no. 7, 6038–6056.     pdf
  A254 Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations (authors: Matteo Bonforte, Antonio Segatti, J. L. V.), Calc. Var. Partial Differential Equations 55 (2016), no. 3, 55-68.     pdf
  A255 Fractional nonlinear degenerate diffusion equations on bounded domains part I. Existence, uniqueness and upper bounds (authors: Matteo Bonforte, J. L. V.), Nonlinear Anal. 131 (2016), 363–398.     pdf
  A256 Finite and infinite speed of propagation for porous medium equations with nonlocal pressure (authors: Diana Stan, Félix del Teso, J. L. V.), J. Differential Equations 260 (2016), no. 2, 1154–1199.     pdf
  A257 Existence of maximal solutions for some very singular nonlinear fractional diffusion equations in 1D (author: J. L. V.), J. Evol. Equ. 16 (2016), 723–758.     pdf
 
2017
  A258 Optimal Existence and Uniqueness Theory for the Fractional Heat Equation (authors: M. Bonforte, Y. Sire, J. L. V.), Nonlin. Anal. TMA, 153 (2017), 142-168.     pdf
  A259 Symmetrization for fractional elliptic and parabolic equations and an isoperimetric application (authors: Yannick Sire, J. L. V., Bruno Volzone), Chinese Annals of Mathematics Ser. B 38 (2017), no. 2, 661-686. (Volume in honor of H. Brezis).     pdf
  A260 Classical solutions and higher regularity for nonlinear fractional diffusion equations (authors: J. L. V., Arturo de Pablo, Fernando Quirós, Ana Rodríguez), J. Eur. Math. Soc. 19 , 7 (2017), 1949-1975.     pdf
  A261 The Fisher-KPP problem with doubly nonlinear diffusion (authors: Alessandro Audrito, J. L. V.), J. Differential Equations 263 (2017), no. 11, 7647--7708. ArXiv:1601.05718.     pdf
  A262 The Fisher-KPP problem with doubly nonlinear "fast" diffusion (authors: Alessandro Audrito, J. L. V.), Nonlinear Analysis TMA, 157 (2017), 212--248.     pdf
  A263 The porous medium equation on Riemannian manifolds with negative curvature. The large-time behaviour (authors: Gabriele Grillo, Matteo Muratori, J. L. V.), Advances in Mathematics 314 (2017), 328-377.     pdf
  A264 Weak and smooth solutions for a fractional Yamabe flow: the case of general compact and locally conformally flat manifolds (authors: Panagiota Daskalopoulos, Yannick Sire, J. L. V.), Comm. Partial Differential Equations 42 (2017), no. 9, 1481--1496. ArXiv:1702.05221.     pdf
  A265 The mathematical theories of diffusion. Nonlinear and fractional diffusion (author: J. L. V.), in "Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions'', Springer Lecture Notes in Mathematics, ISBN 978-3-319-61493-9. C.I.M.E. Foundation Subseries; course held in Cetraro, Italy 2016.     pdf
 
2018
  A266 Flatness implies smoothness for solutions of the porous medium equation (authors: Clemens Kienzler, Herbert Koch, J. L. V.), Cal. Var. PDEs 57, 1 (2018), 57:18. ArXiv:1609.09048v1.     pdf
  A267 Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains (authors: M. Bonforte, A. Figalli, J. L. V.), Analysis of PDEs 11 (2018), no. 4, 945--982. arXiv:1610.09881.     pdf
  A268 Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations (authors: M. Bonforte, A. Figalli, J. L. V.), Calc. Var. Partial Differential Equations 57 (2018), no. 2, 57--57. ArXiv:1710.02731.     pdf
  A269 Asymptotic behaviour for the Fractional Heat Equation in the Euclidean space (author: J. L. V.), in CVEE (Complex Variables and Elliptic Equations), Special volume in honor of Vladimir I. Smirnov's 130th anniversary, 63 (2018),no. 7-8, 1216--1231. ArXiv:1708.00821 [math.AP].     pdf
  A270 Porous medium equation with nonlocal pressure (authors: D. Stan, F. del Teso, J. L. V.), Current Research in Nonlinear Analysis, In Honor of Haim Brezis and Louis Nirenberg, Rassias, T. M. (Ed.), Springer Optim. Appl. 135 Springer, Cham, 2018, pp. 277--308. ArXiv:1801.04244.     pdf
  A271 The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach (authors: J. I. Díaz, D. Gómez-Castro, J. L. V.), Nonlinear Analysis 177 (2018), 325--360; arXiv 1804.08398v1.     pdf
  A272 Porous medium equation with nonlocal pressure in a bounded domain (authors: Quoc-Hung Nguyen, J. L. V.), Comm. PDEs, (2018), 1--38; arXiv:1708.00660 [math.AP].     pdf
  A273 G. I. Barenblatt in Memoriam (1927-2018) (authors: Michiel Bertsch, Alexandre J. Chorin, Nigel Goldenfeld, J. L. V.), Newsletter of the European Mathematical Society 109 (2018) 33--38.     pdf
 
2019. To appear
  A274 The porous medium equation on manifolds with very negative curvature (authors: G. Grillo, M. Muratori, J. L. V.), Math. Annalen, Online 1 may 2018. arXiv:1710.06399 [math.AP].     pdf
  A275 Existence of weak solutions for a general porous medium equation with nonlocal pressure (authors: Diana Stan, Félix del Teso, J. L. V.), Arch. Rat. Mechanics Anal., First Online: 09 February 2019,  to apppear in print;   arXiv:1609.05139.     pdf
  A276 Equivalence of radial solutions of different parabolic gradient-diffusion equations and applications (authors: M. Parviainen, J. L. V.), to appear in Annali Scuola Norm. Sup. Pisa; arXiv:1801.00613.     pdf
 
Preprints in arXiv
  Ar1 Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian (author: J. L. V.), arXiv:1706.10034 [math.AP].     pdf
  Ar2 Asymptotic behaviour for the Heat Equation in Hyperbolic Space (author: J. L. V.), arXiv:1811.09034 [math.AP]     pdf
  Ar3 The fractional Schrödinger equation with singular potential and measure data (authors: David Gómez-Castro, J. L. V.), arXiv:1811.09034 [math.AP]     pdf
  Ar4 Travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains (authors: Alessandro Audrito, J. L. V.), arXiv:1901.03537 [math.AP]     pdf
  Ar5 On a fractional thin film equation (authors: Antonio Segatti, J. L. V.), arXiv:1902.01264 [math.AP]     pdf
   

Research Books after 2000

  B1 The Porous Medium Equation. Mathematical Theory (author: J. L. V.), Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. English, xxii+624 pages. ISBN-10: 0-19-856903-3, ISBN-13: 978-0-19-856903-9.     pdf
  B2 Smoothing and Decay Estimates for Nonlinear Diffusion Equations. Equations of Porous Medium Type (author: J. L. V.), Oxford University Press, Oxford Lecture Series, 2006. English, 248 pp. ISBN-10: 0-19-920297-4, ISBN-13: 978-0-19-920297-3.     pdf
  B3 A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach (authors: Victor A. Galaktionov, J. L. V.), Birkhäuser Verlag, PNLDE 56 (Progress in Non-Linear Differential Equations and Their Applications), 2003. English, 391 pages (xxii+377 pp). ISBN 0-8176-4146-7.     pdf
  B4 Senderos de la ciencia. Del operador Laplaciano a los procesos difusivos no lineales''} [From the Laplacian Operator to Nonlinear Diffusive Processes] (author: J. L. V.), Discurso de ingreso en la Real Academia de Ciencias Exactas, Físicas y Naturales [Inaugural address as member of the Spanish Royal Academy of Sciences], March 26, 2014. Spanish. ISBN: 978-84-695-9782-8.     pdf
  BE4 Recent Trends in Partial Differential Equations (editors: J. L. V., Xavier Cabré, José Antonio Carrillo ), American Mathematical Society, 123 pages, Series: Contemporary Mathematics, no. 409, 2004. ISBN-10: 0-8218-3891-1 ISBN-13: 978-0-8218-3891-4.     pdf
  BE5 Free boundary problems: the forefront of current and future developments (authors, editors: Gui-Qiang Chen, Henrik Shahgholian, J. L. V. ), Phil. Trans. Royal Soc. A 373: 20140285 (2015, volume 373, issue 2050). http://dx.doi.org/10.1098/rsta.2014.0285.     pdf
   

Conference Proceedings after 2000

  C16 A two phase free boundary problem from combustion: uniqueness and agreement of solution (authors: Claudia Lederman, J. L. V., Noemi I. Wolanski), Free boundary problems: theory and applications, I (Chiba, 1999), 180–189, GAKUTO Internat. Ser. Math. Sci. Appl., 13, Gakkōtosho, Tokyo, 2000.     pdf
  C17 From kinetic systems to diffusion equations (authors: Salvarani, F., J. L. V.), "WASCOM 2003''—12th Conference on Waves and Stability in Continuous Media, 475–481, World Sci. Publ., River Edge, NJ, 2004.     pdf
  C18 Partial differential equations and dynamical systems (authors: J. L. V.), (Spanish) Mathematical contributions in honor of Professor Enrique Outerelo Domínguez, 391–406, Homen. Univ. Complut., Editorial Complutense, Madrid, 2004.     pdf
  C19 The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation (author: J. L. V.), Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 15 (2004), no. 3-4, 281–300.     pdf
 

Expository papers and other articles

  E1 Mathematics and the goals of the Year 2000 Program. A call to Spanish mathematicians (author: J. L. V.), (Las matemáticas y los objetivos del año 2000. Un llamamiento a los matemáticos españoles) (in Spanish), Gac. R. Soc. Mat. Esp. 3 (2000), no. 1, 9–22.     pdf
 
  E2 Mathematical Events in Spain in the Year 2000 (author: J. L. V.), Intelligencer, Springer, July 2000, pp. 12-14.     pdf
 
  E3 Pasar sin rozar. Mecánica de fluidos (author: J. L. V.), en "Fotografiando las Matemáticas" (Spanish), Carroggio SA de Eds, (Spanish) Madrid 2000, pp. 92-95.     pdf
 
  E4 The importance of Mathematics in the development of Science and Technology (author: J. L. V.), Boletín Soc. Esp. Mat. Aplicada 9 (2001) 69-112.     pdf
 
  E5 Matemáticas, ciencia y tecnología: una relación profunda y duradera (author: J. L. V.), (Spanish) Encuentros Interdisciplinares, no. 11, vol. IV (2002), 22-38. Portuguese version : Matemática, Ciência e Tecnologia: uma relaçao profunda e duradoura. Boletim da Sociedade Portuguesa de Matemática, 49 (2003), 19-70.     pdf
 
  E6 Miguel de Guzmán, maestro de matemáticos (author: J. L. V.), (Spanish) SUMA 46 (2004), pp. 17-21.     pdf
 
  E7 The Navier-Stokes equation: a physico-mathematical challenge for the XXIst century (author: J. L. V.), Millennium problems, (Spanish) 31–56, Monogr. Real Acad. Ci. Exact. Fís.-Quím. Nat. Zaragoza, 26 , Zaragoza, 2004.     pdf
 
  E8 Volumen dedicado a las Matemáticas Interdisciplinares el siglo XXI (authors: A. Quirós, J. L. V.), (Spanish) Revista Encuentros Multidisciplinares, vol. VIII, no 23, 2006.     pdf
 
  E9 Sin matemáticas no hay paraíso. Saber de números y fórmulas está de moda (author: J. L. V.), (Spanish) artículo publicado en el diario La Nueva España de Oviedo, sección Opinión, 4 Feb. 2009.     pdf
 
  E10 Article in "Recalling James Serrin'' (author: J. L. V.), (Howard Levine and Hans Weinberger, Coordinating Editors) Notices of the AMS 60, no. 6 (2013), 709-710.     pdf
 
  E11 Las Matemáticas y sus aplicaciones, ayer y hoy. Retos del futuro (author: J. L. V.), (Spanish) Revista Encuentros Multidisciplinares, no. 45, Sept-Dic. 2013. Pp. 2-13.     pdf
 
  E12 En memoria de G. I. Bárenblatt (1927-2018). Una historia de ciencia y amistad entre dos mundos (author: J. L. V.), (Spanish) Obituario aparecido en el Boletín electrónico de SEMA, no. 20, julio de 2018, pp 40-43. Reimpresión del artículo aparecido en La Nueva España de Oviedo, 1 de julio de 2018.     pdf