Adapting the time-step to recover the asymptotic behavior in a blow-up problem
Pablo Groisman
Abstract
The equation ut = Δu + up 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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