Weak formulation for singular diffusion equation with dynamic boundary condition
Analysis of PDEs
2017-05-09 v1
Abstract
In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.
Cite
@article{arxiv.1705.02546,
title = {Weak formulation for singular diffusion equation with dynamic boundary condition},
author = {Ryota Nakayashiki and Ken Shirakawa},
journal= {arXiv preprint arXiv:1705.02546},
year = {2017}
}
Comments
23 pages