Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model
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Date
2022-05-13
Authors
Ding, Hang
Zhou, Jun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Parabolic problem of Kirchhoff type, Hyperbolic space, Poincare ball model, Global solution, Blow-up
Citation
Ding, H., & Zhou, J. (2022). Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model. <i>Electronic Journal of Differential Equations, 2022</i>(38), pp. 1-30.
Rights
Attribution 4.0 International