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

Pablo Groisman
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Abstract

The equation $u_t = Δu + u^p$ 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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Pablo Groisman. 2004-07-19. Adapting the time-step to recover the asymptotic behavior in a blow-up problem. https://arxiv.org/abs/math/0407329

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