COURSE NOTES, BOOKS  and SURVEYS
 

NOTES

"The free boundary problem for the heat equation with fixed gradient condition".
Describes the Free Boundary model  for heat propagation used in combustion  to model
deflagration flames, according to Zeldovich and Frank-Kamnetski. Survey presented to the 
International Conference on Free Boundary Problems, Zakopane,  Poland , 1995,   pdf file

"Asymptotic behaviour for the Porous Medium Equation in the whole space" .
 Asymptotic methods and self-similarity at work for the nonlinear heat equation.
Or, "when the Gaussian distribution does not apply". Ph. D. Course,  1996/97.
Fully updated version appeared in  Journal of Evolution Equations,  3 (2003), pp. 67-118
[volume in honor of Prof. Bénilan]. 
Updated Pdf file

 "Asymptotic behaviour for the PME in a bounded domain. The Dirichlet problem" 
 Similar analysis taking into acccount the influence of  absorbing boundary conditions on 
a bounded domain. Ph. D. Course,  1996/97.  Pdf file

"Symmetrization and Mass  Comparison for Degenerate Nonlinear
Parabolic and  related Elliptic Equations",

The techniques of symmetrization and mass concentration comparison applied to nonlinear
elliptic and parabolic equations. Part of a Ph D Course.
Appeared in Advanced Nonlinear Studies.
5 (2005),  87--131
 Pdf file

"Las ecuaciones de la filtracion de fluidos en los medios porosos'',  in Spanish; 
 A survey of modeling of flows though porous media based on Darcy's law: dam problem, 
gas filtration, Boussinesq seepage equation, Muskat-Leverett model, Richards equation. 
Plus a primer on the mathematics of the PME.  Boletin de la  SEMA,  1999.  Pdf file

"The problem of blowup in nonlinear parabolic equations",
 by V.A. Galaktionov and J. L. Vazquez

Course  given in  CIMPA Summer School, Temuco, Chile, 1999.
Appeared  in Discrete and Continuous 
Dynamical Systems - Series A in 2002.
A presentation of the problems of Bow-up Theory for nonlinear heat equations,
plus an update on progress by the authors and others up to 2000. 
Pdf file

"An Introduction to the mathematical theory of the Porous Medium Equation" 
 in Shape Optimization and Free Boundaries (Montreal, PQ, 1990), 347--389, 
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 380, Kluwer Acad. Publ., Dordrecht, 1992
Pdf file

        BOOK ON FLUID MECHAMICS

Un curso de Mecánica de Fluidos, impartido a estudiantes de matemáticas en la Univ. Autónoma 
 de Madrid, in Spanish. Presentation of the theory from a solid mathematical point of view. Suitable as 
introduction to advanced courses on the mathematics of fluids. UAM 1997-2003. This text has been updated
in 2003. Most of the revised course is available in 
   *   mec10chap, ps file,  pdf file 200 pages.  Presentation, general plan and the  basic course, 
10 chapters. Final form. Updated 28.may.2003
   *   mecRest, ps file, pdf file contains advanced chapters on ideal fluids: potentials, complex methods and vorticity
and one on boundary layers for viscous fluids. Appendices, biblio and index. Updated 28.may.2003.
   *  Pending: advanced chapter on viscous fluids, in preparation.
  The author welcomes comments and corrections from interested readers. Updates will take place
while this course is taught in the spring of 2003.