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

Alexander Gladkov

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arXiv · 1611.05273

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

Alexander Gladkov

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Abstract

In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. 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.

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Alexander Gladkov. 2016-11-16. Blow-up problem for semilinear heat equation with nonlinear nonlocal Neumann boundary condition. https://arxiv.org/abs/1611.05273

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