11 citations · 27 across the 16 of their papers we have counts for
16 papers
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…
Periodic solutions to Kobayashi--Warren--Carter systems
Shodai Kubota, Ken Shirakawa
In this paper, a system of parabolic PDEs, called the Kobayashi--Warren--Carter system, is considered as a possible phase-field model of planar grain boundary motion. The Main Theo…
Existence of solutions to a phase-field model of 3D-grain boundary motion governed by a regularized 1-harmonic type flow
Salvador Moll, Ken Shirakawa, Hiroshi Watanabe
In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existenc…
Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi--Warren--Carter Type Models of Grain Boundary Motions
Harbir Antil, Shodai Kubota, Ken Shirakawa +1
In this paper, we consider a class of optimal control problems governed by state-equations of Kobayashi--Warren--Carter type. The control is given by physical temperature. The focu…
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…
Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems
Harbir Antil, Shodai Kubota, Ken Shirakawa +1
This paper is devoted to the study of a class of optimal control problems governed by 1-D Kobayashi-Warren-Carter type systems, which are based on a phase-field model of grain boun…
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…
A class of parabolic systems associated with optimal controls of grain boundary motions
Harbir Antil, Ken Shirakawa, Noriaki Yamazaki
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain b…
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…
Energy dissipative solutions to the Kobayashi-Warren-Carter system
Salvador Moll, Ken Shirakawa, Hiroshi Watanabe
In this paper we study a variational system of two parabolic PDEs, called the Kobayashi-Warren-Carter system, which models the grain boundary motion in a polycrystal. The focus of…
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…
Phase-field systems for grain boundary motions under isothermal solidifications
Ken Shirakawa, Hiroshi Watanabe, Noriaki Yamazaki
Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "-- model" proposed by Kob…
Global monodromy modulo 5 of quintic-mirror family
Kennichiro Shirakawa
The quintic-mirror family is a well-known one-parameter family of Calabi-Yau threefolds. A complete description of the global monodromy group of this family is not yet known. In th…