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arXiv · 1705.02546

Weak formulation for singular diffusion equation with dynamic boundary condition

Ryota Nakayashiki·Ken Shirakawa
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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.

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Ryota Nakayashiki, Ken Shirakawa. 2017-05-07. Weak formulation for singular diffusion equation with dynamic boundary condition. https://arxiv.org/abs/1705.02546

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