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

2004/07/19 by Pablo Groisman, Groisman, Pablo
Computer Science · Engineering · Mathematics · #35B40 #35K60 #65M20 #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0407329

openalex publication_date 2004/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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