1 citations · 2 across the 7 of their papers we have counts for
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A Class of Initial-Boundary Value Problems Governed by Pseudo-Parabolic Weighted Total Variation Flows
Toyohiko Aiki, Daiki Mizuno, Ken Shirakawa
In this paper, we consider a class of initial-boundary value problems governed by pseudo-parabolic total variation flows. The principal characteristic of our problem lies in the ve…
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…
Kobayashi--Warren--Carter type systems with nonhomogeneous Dirichlet boundary data for crystalline orientation
Salvador Moll, Ken Shirakawa, Hiroshi Watanabe
In this paper we study the Dirichlet problem for the Kobayashi--Warren--Carter system. This system of parabolic PDE's models the grain boundary motion in a polycrystal with a presc…
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…
Energy-dissipation in a coupled system of Allen-Cahn type equation and Kobayashi-Warren-Carter type model of grain boundary motion
Hiroshi Watanabe, Ken Shirakawa
In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "-- model" of grain boundary motion, pro…
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…