GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX

doi:10.1016/S0252-9602(11)60268-3

Abstract

Abstract:

This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel'dovich-Kompaneetz-Barenblatt profile.

Key words: Critical global existence curve, degenerate parabolic systems, critical Fujita curve, nonlinear boundary flux, blow-up

CLC Number:

35K55

CHEN Bo-Tao, MI Yong-Sheng, MU Chun-Lai. GLOBAL EXISTENCE AND NONEXISTENCE FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX[J].Acta mathematica scientia,Series B, 2011, 31(2): 681-693.

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