Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2014.02.26
  • Published : 2016.01.01
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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

Acknowledgement

Supported by : China NSF, China Postdoctoral Science Foundation, Shanxi Provincial Postdoctoral Science Foundation, Xi An University of Science and Technology

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