On Solutions of a Parabolic Equation with Nonstandard Growth Condition. (2nd June 2020)

• Record Type: Journal Article
• Authors: Zhan, Huashui
• Other Names: Ragusa Maria Alessandra Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-06-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/9397620
• Languages: English
• ISSNs: 2314-8896

Abstract

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.