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Roles of weight functions in a nonlinear nonlocal parabolic system. (English) Zbl 1138.35340
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:
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35B33Critical exponents (PDE)
35K55Nonlinear parabolic equations