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Indexed by:期刊论文

Date of Publication:2011-09-01

Journal:ANNALI DI MATEMATICA PURA ED APPLICATA

Included Journals:Scopus、SCIE

Volume:190

Issue:3

Page Number:525-537

ISSN No.:0373-3114

Key Words:Variable exponents; Semilinear parabolic system; Maximal solutions; Blow-up; Global solutions; Fujita type conclusion

Abstract:This paper deals with semilinear parabolic equations coupled via variable sources, subject to the homogeneous Dirichlet condition in a bounded domain. Since the variable exponents in the sources are just assumed to be positive, the non-linearities may be non-Lipschitz. We establish the existence-uniqueness with comparison principle of local solutions to the regularized problem at first, and then consider the maximal solutions of the original problem as the limits of the solutions of the regularized problem. Some criteria are established for distinguishing global and non-global solutions of the problem, dependent or independent of initial data. Especially, we prove a Fujita type conclusion that the solutions blow up for any non-trivial initial data under certain assumptions on the variable sources and the size of the domain.