Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation

Koichi Anada, Tetsuya Ishiwata

研究成果: Article査読

5 被引用数 (Scopus)

抄録

We consider initial-boundary value problems for a quasi linear parabolic equation, 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 supθ⁡k(θ,t)≈(T−t)−1log⁡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.

本文言語English
ページ(範囲)181-271
ページ数91
ジャーナルJournal of Differential Equations
262
1
DOI
出版ステータスPublished - 2017 1 5

ASJC Scopus subject areas

  • 分析
  • 応用数学

フィンガープリント

「Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル