Geodesic
Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions
Electronic journal of differential equations, Tome 2013 (2013)
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.
Classification : 35K20, 35B44
Keywords: parabolic system, nonlinear nonlocal boundary condition, blow-up, global solution 
@article{EJDE_2013__2013__a60,
     author = {Sen,  Zhou and Yang,  Zuodong},
     title = {Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.35310},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a60/}
}
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%A Yang,  Zuodong
%T Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions
%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a60/
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%F EJDE_2013__2013__a60
Sen,  Zhou; Yang,  Zuodong. Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a60/