Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions

Abstract

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.

Keywords

• Parabolic system
• nonlinear nonlocal boundary condition
• blow-up
• global solution