Geodesic
Global existence and blow-up of solutions for parabolic systems with nonlinear nonlocal boundary conditions
Electronic Journal of Differential Equations, Tome 2013 (2013).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 35K20, 35B44
Keywords: parabolic system, nonlinear nonlocal boundary condition, blow-up, global solution 
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     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},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a60/}
}
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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/