Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609231 | Journal of Differential Equations | 2017 | 91 Pages |
Abstract
We consider initial-boundary value problems for a quasi linear parabolic equation, kt=k2(kθθ+k)kt=k2(kθθ+k), with zero Dirichlet boundary conditions and positive initial data. It has known that each of solutions blows up at a finite time with the rate faster than (T−t)−1. In this paper, it is proved that supθk(θ,t)≈(T−t)−1loglog(T−t)−1 as t↗Tt↗T under some assumptions. Our strategy is based on analysis for curve shortening flows that with self-crossing brought by S.B. Angenent and J.J.L. Velázquez. In addition, we prove some of numerical conjectures by Watterson which are keys to provide the blow-up rate.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Koichi Anada, Tetsuya Ishiwata,