Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model
| dc.contributor.author | Ding, Hang | |
| dc.contributor.author | Zhou, Jun | |
| dc.date.accessioned | 2023-04-17T21:05:53Z | |
| dc.date.available | 2023-04-17T21:05:53Z | |
| dc.date.issued | 2022-05-13 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 30 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16597 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Parabolic problem of Kirchhoff type | |
| dc.subject | Hyperbolic space | |
| dc.subject | Poincare ball model | |
| dc.subject | Global solution | |
| dc.subject | Blow-up | |
| dc.title | Global solutions and blow-up for a Kirchhoff-type problem on a geodesic ball of the Poincare ball model | |
| dc.type | Article |