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

Alexander Gladkov

doi:10.3934/cpaa.2017101

Article Contents

2017, Volume 16, Issue 6: 2053-2068. Doi: 10.3934/cpaa.2017101

This issue Previous Article Sharp Strichartz estimates in spherical coordinates Next Article Multiplicity results for fractional systems crossing high eigenvalues

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

Alexander Gladkov

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

Received: November 30, 2016

Revised: February 28, 2017

Published: September 2017

This work is supported by the state program of fundamental research of Belarus, grant 1.2.03.1

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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 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.

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Mathematics Subject Classification: Primary: 35B44, 35K58, 35K61.

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