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Global and blow-up solutions for a mutualistic model

โœ Scribed by Peng Feng

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

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โœฆ Synopsis

We study the global and blow-up solutions for a strong degenerate reaction-diffusion system modeling the interactions of two biological species. The local existence and uniqueness of a classical solution are established. We further give the critical exponent for reaction and absorption terms for the existence of global and blow-up solutions. We show that the solution may blow up if the intraspecific competition is weak. This supports ecologist A.J. Nicholson's conclusion that intraspecific competition is the main factor regulating population size.

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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