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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in a"e(2)

Language

English

Abstract

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains ω in R 2 whose solutions blow up in finite time. Of particular interest are the cases where ω = R 2 or ω is a sectorial domain in R 2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the solution of the resulting system of semilinear ODEs. The theoretical results are illustrated by a broad range of numerical examples. © 2011 Springer Science+Business Media, LLC.

Keywords

Adaptive time-stepping, Finite difference spatial discretization, Finite-time blow-up, Local nonlinear boundary conditions, Sectorial domains, Semilinear PDEs, Unbounded spatial domains

Publication Date

2011

Source Publication Title

Journal of Scientific Computing

Volume

49

Issue

3

Start Page

367

End Page

382

Publisher

Springer

ISSN (print)

08857474

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