On the Boundary Value Condition of an Isotropic Parabolic Equation

Abstract EN

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=1Naix,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.