Adapting the time-step to recover the asymptotic behavior in a blow-up problem
Pablo Groisman · arXiv (Cornell University) · 2004
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.