On the Boundary Value Condition of an Isotropic Parabolic Equation. (27th November 2020) - Ou, Qitong; Zhan, Huashui
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.