TEXTBOOK ON THE PME
"The Porous Medium Equation. Mathematical
To be published by
Oxford Univ. Press, preface, index and
if interested in the draft contact the author. OUP catalogue
"Smoothing and Decay Estimates for
Equations of Porous Medium Type"
To be published by
Oxford Univ. Press, cover
preface and chapter
>THE BOOK FROM 2004
"A Stability Technique for Evolution Partial
A Dynamical Systems Approach",
Authors: Victor A. Galaktionov
(Bath, UK) and Juan L. Vázquez (UAM,
A course on dynamical systems
methods for the asymptotic analysis
of partial differential equations. Contains mostly the
the authors to the theory by means
of the so-called S-Theorem
Published by Birkhauser Verlag,
377 pages , 6 1/8 x 9, 10 illus.,
ISBN: 0-8176-4146-7, See
in Birkhauser Website
"The free boundary
problem for the
with fixed gradient condition".
Describes the Free Boundary model for
propagation used in combustion to model
deflagration flames, according to Zeldovich
Frank-Kamnetski. Survey presented to the
International Conference on Free Boundary
Zakopane, Poland , 1995,
Equation in the whole space" .
Asymptotic methods and
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
in honor of Prof. Bénilan].
Updated Pdf file
behaviour for the
a bounded domain. The Dirichlet problem"
Comparison for Degenerate Nonlinear
Similar analysis taking into acccount
influence of absorbing boundary conditions on
a bounded domain. Ph. D. Course,
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
"Las ecuaciones de la
fluidos en los medios porosos'', in Spanish;
survey of modeling of flows though porous
media based on Darcy's law: dam problem,
Boussinesq seepage equation,
Muskat-Leverett model, Richards equation.
primer on the mathematics of the PME.
Boletin de la SEMA, 1999. Postscript
"The problem of
blowup in nonlinear
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.
of the problems of Bow-up Theory for nonlinear heat equations,
update on progress by the authors and others up to 2000. Postscript file
Introduction to the
of the Porous Medium Equation"
in Shape Optimization and Free
(Montreal, PQ, 1990), 347--389,
NATO Adv. Sci. Inst. Ser. C Math. Phys.
380, Kluwer Acad. Publ., Dordrecht, 1992
SOON TO BE COMPLETE
Un curso de
a estudiantes de matemáticas en la Univ. Autónoma
de Madrid, in Spanish.
of the theory from a solid mathematical point of view. Suitable as
introduction to advanced courses on the
of fluids. UAM 1997-2003. This text has been updated
in 2003. Most of the revised course is
mec10chap, ps file, pdf file
200 pages. Presentation,
general plan and the basic course,
10 chapters. Final form. Updated
ps file, pdf file contains
advanced chapters on ideal fluids:
complex methods and vorticity
and one on boundary layers for viscous fluids. Appendices,
and index. Updated 28.may.2003.
* Pending: advanced chapter on viscous
The author welcomes comments and corrections from
readers. Updates will take place
while this course is taught in the spring of 2003.