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

Fei Liang
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회지 (Journal of the KMS)|제53권 제1호|pp. 27-43

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참고문헌

키워드

blow-upblow-up ratenonlocal boundary conditionsdegenerate reaction-diffusion system
주제분류수학

초록

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.

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.

참고문헌 (27)

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