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math.AP2023
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…
math.AP2021
Subdifferential decomposition of 1D-regularized total variation with nonhomogeneous coefficients
Shodai Kubota
In this paper, we consider a convex function defined as a 1D-regularized total variation with nonhomogeneous coefficients, and prove the Main Theorem concerned with the decompositi…
math.AP2020
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…