关键词: porous medium equation, convection, global inequality of Harnack type, BCP estimates, initial trace

Abstract:

In this paper author consider the following problem
u_t=△u^m+b_i(uⁿ)_xi
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