On Solutions of a Parabolic Equation with Nonstandard Growth Condition. (2nd June 2020) - Zhan, Huashui
Abstract : A parabolic equation with nonstandard growth condition is considered. A kind of weak solution and a kind of strong solution are introduced, respectively; the existence of solutions is proved by a parabolically regularized method. The stability of weak solutions is based on a natural partial boundary value condition. Two novelty elements of the paper are both the dependence of diffusion coefficient b x, t on the time variable t, and the partial boundary value condition based on a submanifold of ∂ Ω × 0, T . How to overcome the difficulties arising from the nonstandard growth conditions is another technological novelty of this paper.