American Institute of Mathematical Sciences

November  2017, 16(6): 2053-2068. doi: 10.3934/cpaa.2017101

Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition

 Department of Mechanics and Mathematics Belarusian State University, Nezavisimosti avenue 4,220030 Minsk, Belarus

Received  December 2016 Revised  March 2017 Published  July 2017

Fund Project: This work is supported by the state program of fundamental research of Belarus, grant 1.2.03.1.

In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence result. We then give some criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data. Finally, we show that under certain conditions blow-up occurs only on the boundary.

Citation: Alexander Gladkov. Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2053-2068. doi: 10.3934/cpaa.2017101
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