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Blow-up properties of solutions for a multi-coupled parabolic system

โœ Scribed by Fengjie Li; Sining Zheng; Bingchen Liu

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
331 KB
Volume
68
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

This paper deals with the blow-up behavior of radial solutions to a parabolic system multi-coupled via inner sources and boundary flux. We first obtain a necessary and sufficient condition for the existence of non-simultaneous blow-up, and then find five regions of exponent parameters where both non-simultaneous and simultaneous blow-up may happen. In particular, nine simultaneous blow-up rates are established for different regions of parameters. It is interesting to observe that different initial data may lead to different simultaneous blow-up rates even with the same exponent parameters.

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## Abstract In this paper the degenerate parabolic system __u__~__t__~=__u__(__u__~__xx__~+__av__). __vt__=__v__(__v__~__xx__~+__bu__) with Dirichlet boundary condition is studied. For $a. b {<} \lambda\_{1} (\sqrt {ab} {<} \lambda\_{1} {\rm if}\, \alpha\_{1} {\neq} \alpha\_{2})$, the global existe