Journal of Scientific Computing

, Volume 49, Issue 3, pp 367–382 | Cite as

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

  • Jiwei Zhang
  • Houde Han
  • Hermann Brunner


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.


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


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Department of MathematicsHong Kong Baptist UniversityKowloon TongP.R. China
  4. 4.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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