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.
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