THE INITIAL TRACE OF SOLUTIONS FOR POROUS MEDIUM EQUATION WITH CONVECTION

Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (S1): 140-153.

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THE INITIAL TRACE OF SOLUTIONS FOR POROUS MEDIUM EQUATION WITH CONVECTION

Lu Guofu

Math. Dept. of Suzhou Univ. & Math. Dept. of Putian College, Putian 351100, China

Received:1995-12-29 Online:1997-12-26 Published:1997-12-26
Supported by:
This work is supported by Natural Science Foundation of Fijian Province & Science Foundation of Putian College

Abstract

Abstract:

In this paper author consider the following problem
u_t=△u^m+b_i(uⁿ)_{x_i}
Let u=u(x.t) be a continuous weak solution of the equation in R^N×(O,T] for some T >O.Then author conclude:corresponding to u there is a unique nonnegative Borel measure v on R^N which is the initial trace of u; there is the global inequality of Harnack type for u; the initial trace must belong to a certain growth class; consequently, by combining the results mentioned above a uniqueness conclusion is established.

Key words: porous medium equation, convection, global inequality of Harnack type, BCP estimates, initial trace

Lu Guofu. THE INITIAL TRACE OF SOLUTIONS FOR POROUS MEDIUM EQUATION WITH CONVECTION[J].Acta mathematica scientia,Series A, 1997, 17(S1): 140-153.

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THE INITIAL TRACE OF SOLUTIONS FOR POROUS MEDIUM EQUATION WITH CONVECTION

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