Search

We consider initial-boundary value problems for a quasi linear parabolic equation, k t = k 2 ( k θ θ + 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 sup θ ⁡ k ( θ , t ) ≈ ( T − t ) − 1 log ⁡ log ⁡ ( T − t ) − 1 as t ↗ 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. [ABSTRACT FROM AUTHOR]