Numerical solution of a fast diffusion equation
Authors:
Marie-Noelle Le Roux and Paul-Emile Mainge
Journal:
Math. Comp. 68 (1999), 461-485
MSC (1991):
Primary 35K55, 35K57, 65M60
DOI:
https://doi.org/10.1090/S0025-5718-99-01063-7
MathSciNet review:
1627805
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, the authors consider the first boundary value problem for the nonlinear reaction diffusion equation: in
, a smooth bounded domain in
with the zero lateral boundary condition and with a positive initial condition,
(fast diffusion problem),
and
. Sufficient conditions on the initial data are obtained for the solution to vanish or become infinite in a finite time. A scheme for the discretization in time of this problem is proposed. The numerical scheme preserves the essential properties of the initial problem; namely existence of an extinction or a blow-up time, for which estimates have been obtained. The convergence of the method is also proved.
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Additional Information
Marie-Noelle Le Roux
Affiliation:
GRAMM-Mathématiques, 351, cours de la Libération, F-33405 Talence Cedex, France
Email:
m.n.leroux@math.u-bordeaux.fr
Paul-Emile Mainge
Affiliation:
GRAMM-Mathématiques, 351, cours de la Libération, F-33405 Talence Cedex, France
DOI:
https://doi.org/10.1090/S0025-5718-99-01063-7
Keywords:
Reaction diffusion equations, parabolic problems
Received by editor(s):
August 13, 1996
Received by editor(s) in revised form:
May 5, 1997
Article copyright:
© Copyright 1999
American Mathematical Society