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Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions. (English) Zbl 1288.35310

Summary: In this article we study a nonlinear parabolic system with nonlinear nonlocal boundary conditions. We prove the uniqueness of the solutions and establish the conditions for global solutions and non-global solutions. It is interesting to observe that the weight function for the nonlocal Dirichlet boundary conditions plays a crucial role in determining whether the solutions are global or blow up in finite time.

MSC:

35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
35B44 Blow-up in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems