7 papers
Large-Time Behavior of Pseudo-Parabolic Equations Associated with Generalized Total Variation Energies
Daisuke Kubota, Daiki Mizuno, Ken Shirakawa +1
In this paper, we study the well-posedness and large-time behavior of a pseudo-parabolic problem associated with a generalized total variation energy in the -framework. A main…
Well-Posedness of Pseudo-Parabolic Gradient Systems with State-Dependent Dynamics
Harbir Antil, Daiki Mizuno, Ken Shirakawa +1
This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fi…
Well-posedness of parabolic KWC-systems with variable-dependent mobilities
Daiki Mizuno, Ken Shirakawa
In this paper, we deal with the parabolic KWC system, associated with the mathematical model of grain boundary motion. The goal of this paper is to guarantee the well-posedness of…
Structure-preserving scheme for 1D KWC system
Makoto Okumura, Shodai Kubota, Ken Shirakawa
In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is th…
Optimal Control of Pseudo-Parabolic KWC Systems for Grain Boundary Motion
Harbir Antil, Daiki Mizuno, Ken Shirakawa
The KWC system is a well-known generic framework for phase-field models of grain boundary motion, whose original formulation is given as a parabolic gradient flow of a free energy.…
A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment
Harbir Antil, Daiki Mizuno, Ken Shirakawa +1
This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic mono…
Well-posedness of a Pseudo-Parabolic KWC System in Materials Science
Harbir Antil, Daiki Mizuno, Ken Shirakawa
The original KWC-system is widely used in materials science. It was proposed in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase field model of planar g…