Ken Shirakawa
Chiba University
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Publication
Featured researches published by Ken Shirakawa.
Proceedings of the International Conference on Nonlinear Analysis | 2008
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
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
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
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
Ken Shirakawa; Rejeb Hadiji
Discrete and Continuous Dynamical Systems - Series S | 2011
Takeshi Ohtsuka; Ken Shirakawa; Noriaki Yamazaki
Asymptotic Analysis | 2004
Pierluigi Colli; Ken Shirakawa
Journal of Mathematical Analysis and Applications | 2012
Masahiro Kubo; Ken Shirakawa; Noriaki Yamazaki
Chinese Annals of Mathematics, Series B | 2006
Pierluigi Colli; Michel Frémond; Elisabetta Rocca; Ken Shirakawa
Calculus of Variations and Partial Differential Equations | 2014
Salvador Moll; Ken Shirakawa