English

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.

Keywords

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

R2 v1 2026-06-22T19:39:18.181Z