ON THE EXISTENCE WITH EXPONENTIAL DECAY AND THE BLOW-UP OF SOLUTIONS FOR COUPLED SYSTEMS OF SEMI-LINEAR CORNER-DEGENERATE PARABOLIC EQUATIONS WITH SINGULAR POTENTIALS

• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（1）
• 页码范围: 257-282
• 页数: 26页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.01.015

摘要

In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner sin-gularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.