INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS

doi:10.1016/S0252-9602(10)60115-4

Abstract

Abstract:

In this note, we study the existence of an initial trace of nonnegative solutions for the following problem
u_t-div(|\bigtriangledown u^m|^p-2\bigtriangledownu^m)+u^q=0 in Q_T=Ω×(0, T).
We prove that the initial trace is an outer regular Borel measure, which may not be locally bounded for some values of parameters p, q, and m. We also study the corresponding Cauchy problems with a given generalized Borel measure as initial data.

Key words: Doubly degenerate, Initial trace, Borel measure

CLC Number:

35K20

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WANG Shu-Juan, ZHAO Jun-Ning. INITIAL TRACE OF SOLUTIONS FOR A DOUBLY NONLINEAR DEGENERATE PARABOLIC EQUATIONS[J].Acta mathematica scientia,Series B, 2010, 30(4): 1174-1188.

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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(10)60115-4

http://121.43.60.238/sxwlxbB/EN/Y2010/V30/I4/1174

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