Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux

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December 2007, 6(4): 1113-1129. doi: 10.3934/cpaa.2007.6.1113

Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux

1.	Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China, China

Received October 2006 Revised February 2007 Published September 2007

Abstract
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This paper deals with non-simultaneous blow-up for heat equations with positive-negative sources coupled via nonlinear boundary flux. At first, we establish the necessary-sufficient conditions for non-simultaneous blow-up of solutions under suitable initial data. Furthermore, the sufficient conditions are determined under which any blow-up of solutions to the model would be non-simultaneous. Comparing with those for a similar system possessing negative-negative sources obtained in a previous paper [19] we show clearly the contribution of the positive source in the present model to the non-simultaneous blowing up behavior of solutions.

Keywords: positive source, negative source, nonlinear boundary flux., Non-simultaneous blow-up, heat equations.

Mathematics Subject Classification: Primary: 35K57, 35B33, 35B4.

Citation: Lan Qiao, Sining Zheng. Non-simultaneous blow-up for heat equations with positive-negative sources and coupled boundary flux. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1113-1129. doi: 10.3934/cpaa.2007.6.1113

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