Electron. J. Differential Equations, Vol. 2022 (2022), No. 38, pp. 130.
Global solutions and blowup for a Kirchhofftype problem on
a geodesic ball of the Poincare ball model
Hang Ding, Jun Zhou
Abstract:
This article concerns a Kirchhofftype parabolic problem on a geodesic ball of hyperbolic
space. Firstly, we obtain conditions for finite time blowup, and for the existence of global
solutions for J(u_0)≤ d, where J(u_{0}) denotes the initial energy and d denotes
the depth of the potential well.
Secondly, we estimate the upper and lower bounds of the blowup time.
In addition, we derive the growth rate of the blowup solution and the
decay rate of the global solution.
Thirdly, we establish a new finite time blowup 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 blowup 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; blowup.
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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

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