On the Boundary Value Condition of an Isotropic Parabolic Equation. (27th November 2020)

• Record Type: Journal Article
• Authors: Ou, Qitong; Zhan, Huashui
• Other Names: Urbina Wilfredo Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-11-27
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/2180830
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. By a generalized Gronwall inequality, the stability of strong solutions to this equation is established, and the uniqueness of weak solutions is proved. Compared with the related works, a new boundary value condition, ∏ i = 1 N a i x, t = 0, x, t ∈ ∂ Ω × 0, T, is introduced the first time and has been proved that it can take place of the Dirichlet boundary value condition in some way.