Affiliation:
1. School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China
2. Fujian Engineering and Research Center of Rural Sewage Treatment and Water Safety, Xiamen 361024, China
Abstract
The initial-boundary value problem of a porous medium equation with a variable exponent is considered. Both the diffusion coefficient ax,t and the variable exponent px,t depend on the time variable t, and this makes the partial boundary value condition not be expressed as the usual Dirichlet boundary value condition. In other words, the partial boundary value condition matching up with the equation is based on a submanifold of ∂Ω×0,T. By this innovation, the stability of weak solutions is proved.
Funder
Natural Science Foundation of Fujian Province