Blow-up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition |
| |
Authors: | Alexander Gladkov Kwang Ik Kim |
| |
Institution: | a Department of Mathematics, Vitebsk State University, Moskovskii pr. 33, 210038 Vitebsk, Belarus b Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea |
| |
Abstract: | In this paper, we consider a semilinear heat equation ut=Δu+c(x,t)up for (x,t)∈Ω×(0,∞) with nonlinear and nonlocal boundary condition and nonnegative initial data where p>0 and l>0. We prove global existence theorem for max(p,l)?1. Some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given. |
| |
Keywords: | Reaction-diffusion equation Nonlocal boundary condition Global solution Blow-up |
本文献已被 ScienceDirect 等数据库收录! |
|