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 |