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

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

2004-07-19

arxiv.org/abs/math/0407329v1

Mathematics

Numerical Analysis

22 pages

Scientific paper

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.

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