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

Fei Liang | Zendy

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

Author(s) -

Fei Liang

Publication year - 2016

Publication title -

journal of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.403

H-Index - 31

eISSN - 2234-3008

pISSN - 0304-9914

DOI - 10.4134/jkms.2016.53.1.027

Subject(s) - degenerate energy levels , mathematics , dirichlet boundary condition , mathematical analysis , nonlinear system , dirichlet distribution , boundary (topology) , boundary value problem , blowing up , diffusion , reaction–diffusion system , physics , quantum mechanics , thermodynamics

This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirich- let 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 determin- ing 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.

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