Blow-up for the heat equation with a general memoryboundary condition

Keng Deng; Zhihua Dong

doi:10.3934/cpaa.2012.11.2147

Article Contents

2012, Volume 11, Issue 5: 2147-2156. Doi: 10.3934/cpaa.2012.11.2147

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Blow-up for the heat equation with a general memory boundary condition

Keng Deng^1, and
Zhihua Dong^2,

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
2.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010

Received: February 28, 2011

Revised: October 31, 2011

Published: August 2012

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Abstract

In this paper, we study the long-time behavior of nonnegative solutions of the heat equation with a general memory boundary condition. We first present conditions on the memory term for finite time blow-up. We then establish global existence results through both analytical and numerical methods. Finally, we show that under certain conditions blow-up occurs only on the boundary.

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Mathematics Subject Classification: Primary: 35B44, 35K05, 35K20.

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