Zhou Sen, Zuodong Yang
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.
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| Zhou Sen Institute of Mathematics, School of Mathematical Sciences Nanjing Normal University, Jiangsu Nanjing 210023, China. College of Sciences, China Pharmaceutical University Jiangsu Nanjing 211198, China | |
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Zuodong Yang Institute of Mathematics, School of Mathematical Sciences Nanjing Normal University, Jiangsu Nanjing 210023, China email: zdyang_jin@263.net |
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