Ding, HangZhou, Jun2023-04-172023-04-172022-05-13Ding, 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. 1-30.1072-6691https://hdl.handle.net/10877/16597This 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.Text30 pages1 file (.pdf)enAttribution 4.0 InternationalParabolic problem of Kirchhoff typeHyperbolic spacePoincare ball modelGlobal solutionBlow-upArticle