Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model

Electronic Journal of Differential Equations

article

Hang Ding¹  Jun Zhou¹ 

[1] School of Mathematics and Statistics Southwest University Chongqing 400715

关键词: Parabolic problem of Kirchhoff type;    hyperbolic space;    poincare ball model;    global solution;    blow-up;   

DOI  :  10.58997/ejde.2022.38

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

This article concerns a Kirchhoff-type parabolic problem on a geodesic ball of hyperbolicspace. Firstly, we obtain conditions for finite time blow-up, and for the existence of globalsolutions for J(u_0)≤ d, where J(u0) denotes the initial energy and d denotes the depth of the potential well.Secondly, we estimate the upper and lower bounds of the blow-up time.In addition, we derive the growth rate of the blow-up solution and the decay rate of the global solution.Thirdly, we establish a new finite time blow-up condition which is independent of d and prove that the solution can blow up in finite time with arbitrary high initial energy, by using this blow-up condition.Finally, we present some equivalent conditions for the solution existing globally or blowing upin finite time.

【 授权许可】

CC BY