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Dive into the research topics where Ken Shirakawa is active.

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Featured researches published by Ken Shirakawa.


Proceedings of the International Conference on Nonlinear Analysis | 2008

WELL-POSEDNESS AND PERIODIC STABILITY FOR QUASILINEAR PARABOLIC VARIATIONAL INEQUALITIES WITH TIME-DEPENDENT CONSTRAINTS

Ken Shirakawa; Masahiro Kubo; Noriaki Yamazaki

We study variational inequalities with time-dependent constraints for quasilinear parabolic PDE of divergence from. Introducing a general condition on the constraints, we prove existence. uniqueness and order property of solution. Some applications are given.


Nonlinearity | 2017

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 the study is on the existence of solutions to this system which dissipate the associated energy functional. We obtain the existence of this type of solution via a suitable approximation of the energy functional with Laplacians and an extra regularization of the weighted total variation term of the energy. As a byproduct of this result, we also prove some -convergence results concerning weighted total variations and the corresponding time-dependent cases. Finally, the regularity obtained for the solutions together with the energy dissipation property, permits us to completely characterize the ω-limit set of the solutions.


Archive | 2017

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 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.


Archive | 2006

Solvability for a PDE Model of Regional Economic Trend

Ken Shirakawa; Akio Ito; Atsushi Kadoya

The aim of this work is to develop a simulation method focused on regional economic trend. In this light, an original model, formulated by partial differential equations, will be proposed. Consequently, the existence of time-local solutions of our mathematical model will be concluded, as a transitional report in the research.


Communications on Pure and Applied Analysis | 2010

Asymptotic analysis for micromagnetics of thin films governed by indefinite material coefficients

Ken Shirakawa; Rejeb Hadiji


Discrete and Continuous Dynamical Systems - Series S | 2011

Optimal control problem for Allen-Cahn type equation associated with total variation energy

Takeshi Ohtsuka; Ken Shirakawa; Noriaki Yamazaki


Asymptotic Analysis | 2004

Attractors for the one‐dimensional Frémond model of shape memory alloys

Pierluigi Colli; Ken Shirakawa


Journal of Mathematical Analysis and Applications | 2012

Variational inequalities for a system of elliptic–parabolic equations

Masahiro Kubo; Ken Shirakawa; Noriaki Yamazaki


Chinese Annals of Mathematics, Series B | 2006

Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys*

Pierluigi Colli; Michel Frémond; Elisabetta Rocca; Ken Shirakawa


Calculus of Variations and Partial Differential Equations | 2014

Existence of solutions to the Kobayashi–Warren–Carter system

Salvador Moll; Ken Shirakawa

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Masahiro Kubo

Nagoya Institute of Technology

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