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http://dx.doi.org/10.4134/JKMS.2016.53.1.027

GLOBAL EXISTENCE AND BLOW-UP FOR A DEGENERATE REACTION-DIFFUSION SYSTEM WITH NONLINEAR LOCALIZED SOURCES AND NONLOCAL BOUNDARY CONDITIONS  

LIANG, FEI (DEPARTMENT OF MATHEMATICS XI AN UNIVERSITY OF SCIENCE AND TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 27-43 More about this Journal
Abstract
This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirichlet boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.
Keywords
degenerate reaction-diffusion system; nonlocal boundary conditions; blow-up; blow-up rate;
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