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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

Lan Qiao 1, and  Sining Zheng 1,

1. 

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

Received  October 2006 Revised  February 2007 Published  September 2007

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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