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SIAM J. on Scientific Computing / Volume 31 / Issue 6

SIAM J. Sci. Comput. 31, pp. 4478-4496 (19 pages)

Computational Solution of Blow-Up Problems for Semilinear Parabolic PDEs on Unbounded Domains

Hermann Brunner, Xiaonan Wu, and Jiwei Zhang

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This paper is concerned with the numerical solution of semilinear parabolic PDEs on unbounded spatial domains whose solutions blow up in finite time. The focus of the presentation is on the derivation of the nonlinear absorbing boundary conditions for one-dimensional and two-dimensional computational domains and on a simple but efficient adaptive time-stepping scheme. The theoretical results are illustrated by a broad range of numerical examples, including problems with multiple blow-up points.

© 2010 Society for Industrial and Applied Mathematics

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KEYWORDS

AMS Subject Headings

65M06, 65L10, 35Q53, 35Q51

PUBLICATION DATA

ISSN

1064-8275 (print)  
1095-7197 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received June 05, 2009
Accepted August 17, 2009
Published online January 20, 2010
Digital Object Identifier
http://dx.doi.org/10.1137/090761367

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