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Zbl 1138.35340
Zheng, Sining; Kong, Linghua
Roles of weight functions in a nonlinear nonlocal parabolic system. (English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 8, A, 2406-2416 (2008). ISSN 0362-546X

Summary: This paper deals with a semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. We establish the conditions for global and non-global solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or non-global, but also whether (for the non-global solutions) the blowing up occurs for any positive initial data or just for large ones.

MSC 2000:: *35K50 Systems of parabolic equations, boundary value problems
35B33 Critical exponents
35K55 Nonlinear parabolic equations

Keywords: nonlocal sources; nonlocal boundary conditions; blow-up; semilinear parabolic system; weighted Dirichlet conditions

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