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  

作　　者：Hua CHEN Nian LIU 陈化;刘念(School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China;School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [2]School of Science,Wuhan University of Technology,Wuhan 430070,China

出　　处：《Acta Mathematica Scientia》2021年第1期257-282,共26页数学物理学报（B辑英文版）

基　　金：supported by NFSC(11871387 and 11931012)。

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 singularities.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.

关 键 词：coupled parabolic equations totally characteristic degeneracy singular potentials asymptotic stability BLOW-UP 

分 类 号：O175.26[理学—数学]