COURSE NOTES, BOOKS  and SURVEYS
 

  
NEW!
      
   
A TEXTBOOK ON THE PME 2006
"The Porous Medium Equation. Mathematical Theory"
To be published by Oxford Univ. Press, preface, index and introductory chapters
if interested in the draft contact the author.
  OUP catalogue page
<>

"Smoothing and Decay Estimates  for Nonlinear Parabolic
Equations  of Porous Medium Type"
To be published by Oxford Univ. Press,  cover     preface and chapter list
OUP  catalogue page


THE BOOK FROM 2004

"A Stability Technique for Evolution Partial Differential Equations.
  A Dynamical Systems Approach",

  Authors:  Victor A. Galaktionov (Bath, UK)  and  Juan L. Vázquez  (UAM, Spain).

  A course on dynamical systems methods for the asymptotic analysis
  of partial differential equations. Contains mostly the contributions of
  the authors to the theory by means of the so-called S-Theorem
Published by Birkhauser Verlag,  2004
377 pages , 6 1/8 x 9, 10 illus., hardcover
ISBN: 0-8176-4146-7, 
See cover   Page in Birkhauser Website

       MORE

"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,   Postscript 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.  Postscript 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.  Postscript 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. 
Postscript 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
Postscript file

        SOON TO BE COMPLETE

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.