SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE

doi:10.1016/S0252-9602(15)30092-8

Abstract

Abstract:

This paper deals with the Cauchy problem for a doubly singular parabolic equa-tion with a weighted source u^t=div(|∇u|^p-2∇u^m)+|x|^αu^q,(x, t)∈R^N×(0, T), where N≥1, 1< p< 2, m>max{0, 3-p-p/N} satisfying 2< p+m< 3, q>1, and α>N(3-p-m)-p.We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem.Moreover, the life span of solutions is also studied.

Key words: life span, secondary critical exponent, doubly singular parabolic equation, weighted source, blow-up

CLC Number:

35K55

Pan ZHENG, Chunlai MU, Xuegang HU, Fuchen ZHANG. SECONDARY CRITICAL EXPONENT AND LIFE SPAN FOR A DOUBLY SINGULAR PARABOLIC EQUATION WITH A WEIGHTED SOURCE[J].Acta mathematica scientia,Series B, 2016, 36(1): 244-256.

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