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CRITICAL EXPONENTS FOR A REACTION–DIFFUSION MODEL WITH ABSORPTIONS AND COUPLED BOUNDARY FLUX

Published online by Cambridge University Press:  15 February 2005

Sining Zheng  and
Fengjie Li
Sining Zheng
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China (snzheng@dlut.edu.cn)
Fengjie Li
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China (snzheng@dlut.edu.cn)
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Abstract

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This paper deals with a reaction–diffusion model with inner absorptions and coupled nonlinear boundary conditions of exponential type. The critical exponents are described via a pair of parameters that satisfy a certain matrix equation containing all the six nonlinear exponents of the system. Whether the solutions blow up or not is determined by the signs of the two parameters. A more precise analysis, depending on the geometry of $\varOmega$ and the absorption coefficients, is proposed for the critical sign of the parameters.

AMS 2000 Mathematics subject classification: Primary 35K55; 35B33

Keywords

critical exponentsnonlinear absorptionnonlinear boundary fluxblow-upglobal boundedness
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 241 - 252
Copyright
Copyright © Edinburgh Mathematical Society 2005