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J. Korean Math. Soc. 2016; 53(1): 27-43

Printed January 1, 2016

https://doi.org/10.4134/JKMS.2016.53.1.27

Copyright © The Korean Mathematical Society.

Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditions

Fei Liang

Xi An University of Science and Technology

Abstract

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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

MSC numbers: 34B10, 35K57, 35K65

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