Affiliation:
1. School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
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,
, is introduced the first time and has been proved that it can take place of the Dirichlet boundary value condition in some way.
Funder
Natural Science Foundation of Fujian Province