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Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in ℝ2

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Abstract

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains Ω in ℝ2 whose solutions blow up in finite time. Of particular interest are the cases where Ω=ℝ2 or Ω is a sectorial domain in ℝ2. 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.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Jiwei Zhang

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Houde Han

  3. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, P.R. China

    Hermann Brunner

  4. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

    Hermann Brunner

Authors
  1. Jiwei Zhang
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  2. Houde Han
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  3. Hermann Brunner
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Correspondence to Hermann Brunner.

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Zhang, J., Han, H. & Brunner, H. Numerical Blow-up of Semilinear Parabolic PDEs on Unbounded Domains in ℝ2 . J Sci Comput 49, 367–382 (2011). https://doi.org/10.1007/s10915-011-9467-5

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  • DOI: https://doi.org/10.1007/s10915-011-9467-5

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