Adapting the time-step to recover the asymptotic behavior in a blow-up problem

Pablo Groisman

Adapting the time-step to recover the asymptotic behavior in a blow-up problem

Numerical Analysis 2007-05-23 v1

Authors: Pablo Groisman

Abstract

The equation $u_t = \Delta u + u^p$ with homegeneous Dirichlet boundary conditions has solutions with blow-up if $p > 1$ . An adaptive time-step procedure is given to reproduce the asymptotic behvior of the solutions in the numerical approximations. We prove that the numerical method reproduces the blow-up cases, the blow-up rate and the blow-up time. We also localize the numerical blow-up set.

Keywords

adaptive time-step blow-up problem numerical approximation asymptotic behavior blow-up rate Dirichlet boundary

Cite

@article{arxiv.math/0407329,
  title  = {Adapting the time-step to recover the asymptotic behavior in a blow-up problem},
  author = {Pablo Groisman},
  journal= {arXiv preprint arXiv:math/0407329},
  year   = {2007}
}

Comments

22 pages

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