The uniqueness of the solution to the diffusion equation with a damping term |
| |
Authors: | Huashui Zhan |
| |
Affiliation: | 1. School of Applied Mathematics, Xiamen University of Technology , Xiamen, P.R. China.2012111007@xmut.edu.cn |
| |
Abstract: | Consider a non-linear diffusion equation with a damping term. If the diffusion coefficient is positive, then the solutions are not unique generally. However, if the diffusion coefficient degenerates, the situation may change. In this paper, not only the existence of the weak solution is established, but also the uniqueness of the weak solutions is proved, even the boundary value condition is not imposed. The conclusions imply that, on the boundary, the degeneracy of diffusion coefficient can eliminate the action from the damping term. |
| |
Keywords: | Diffusion equation boundary value condition damping term uniqueness |
|
|