具有多重非线性的非牛顿多方渗流方程的整体存在性与非存在性

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Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic System with Nonlinear Boundary Conditions

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Abstract:

This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear diffusion, nonlinear reaction and nonlinear boundary flux in a parabolic model with multiple nonlinearities. We obtain the critical global existence curve and critical Fujita curve by constructing various self-similar supersolutions and subsolu-tions.

Key words: Ritical global existence curve, Degenerate parabolic equation, Critical Fujita curve, Non-Newtonian polytropic
filtration equation, Blow-up

CLC Number:

35K55

MI Yong-Sheng, MU Chun-Lai, WU Yun-Long. Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic System with Nonlinear Boundary Conditions[J].Acta mathematica scientia,Series A, 2014, 34(3): 626-637.

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