• 제목/요약/키워드: nonlocal reaction-diffusion system

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NEW BLOW-UP CRITERIA FOR A NONLOCAL REACTION-DIFFUSION SYSTEM

  • Kim, Eun-Seok
    • 호남수학학술지
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    • 제43권4호
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    • pp.667-678
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    • 2021
  • Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

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

  • LIANG, FEI
    • 대한수학회지
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    • 제53권1호
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    • pp.27-43
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    • 2016
  • 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.