School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: hding0527@163.com
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: jzhouwm@163.com
Hang Ding, Jun Zhou
Abstract:
This article concerns a Kirchhoff-type parabolic problem on a geodesic ball of hyperbolic
space. Firstly, we obtain conditions for finite time blow-up, and for the existence of global
solutions 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 up
in finite time.
Submitted July 18, 2021 Published May 13, 2022.
Math Subject Classifications: 35K55, 35B40, 35B44.
Key Words: Parabolic problem of Kirchhoff type; hyperbolic space;
poincare ball model; global solution; blow-up.
DOI: https://doi.org/10.58997/ejde.2022.38
Show me the PDF file (447 KB), TEX file for this article.
|
Hang Ding School of Mathematics and Statistics Southwest University Chongqing 400715, China email: hding0527@163.com |
|---|---|
|
Jun Zhou School of Mathematics and Statistics Southwest University Chongqing 400715, China email: jzhouwm@163.com |
Return to the EJDE web page