Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 224, pp. 1-12.

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

Authors: Zhou Sen     (Nanjing Normal Univ., Jiangsu, China)
         Zuodong Yang (Nanjing Normal Univ., Jiangsu, China)

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.


Submitted December 12, 2012. Published October 11, 2013.
Math Subject Classifications: 35K20, 35B44.
Key Words: Parabolic system; nonlinear nonlocal boundary condition; 
           blow-up; global solution.