Mathematics – Analysis of PDEs
Scientific paper
2011-02-21
Mathematics
Analysis of PDEs
Changes to the previous version: Theorem 4 was changed to cover the case N=2 instead of N=1. Section 3 has therefore been rewr
Scientific paper
The aim of this paper is to refine some results concerning the blow-up of solutions of the exponential reaction-diffusion equation. We consider solutions that blow-up in finite time, but continue to exist as weak solutions beyond the blow-up time. The main result is that these solutions become regular immediately after the blow-up time. This result improves on that of Fila, Matano and Pol\'acik, who consider radially nonincreasing solutions, whereas no such assumption is needed here. Under certain additional assumptions we also obtain that the regularization is asymptotically selfsimilar. Moreover, we consider the question of blow-up rate for radial solutions of the two-dimensional problem and prove that the blow-up is of type I, provided that the maximum of the solution is attained at the origin.
No associations
LandOfFree
Some comments concerning the blow-up of solutions of the exponential reaction-diffusion equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Some comments concerning the blow-up of solutions of the exponential reaction-diffusion equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some comments concerning the blow-up of solutions of the exponential reaction-diffusion equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-520979