5 papers
Kobayashi-Warren-Carter System of Singular Type under Dynamic Boundary Condition
Ryota Nakayashiki, Ken Shirakawa
In this paper, we consider a coupled system, known as Kobayashi--Warren--Carter system, abbreviated as the KWC system. KWC system consists of an Allen--Cahn type equation and a sin…
Optimal control problems for 1D parabolic state-systems of KWC types with dynamic boundary conditions
Shodai Kubota, Ryota Nakayashiki, Ken Shirakawa
In this paper, we consider a class of optimal control problems governed by 1D parabolic state-systems of KWC types with dynamic boundary conditions. The state-systems are based on…
On boundary detachment phenomena for the total variation flow with dynamic boundary conditions
Yoshikazu Giga, Ryota Nakayashiki, Piotr Rybka +1
We combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions. We analyze the behavior of facets at the parts of the bou…
Weak formulation for singular diffusion equation with dynamic boundary condition
Ryota Nakayashiki, Ken Shirakawa
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 b…
A class of quasi-linear Allen-Cahn type equations with dynamic boundary conditions
Pierluigi Colli, Gianni Gilardi, Ryota Nakayashiki +1
In this paper, we consider a class of coupled systems of PDEs, denoted by (ACE) for . For each , the system (ACE)$_{\var…