Related papers: Kobayashi-Warren-Carter System of Singular Type un…
In this paper, we consider a system of initial boundary value problems for parabolic equations, as a generalized version of the "$ \phi $-$ \eta $-$ \theta $ model" of grain boundary motion, proposed by Kobayashi [16]. The system is a…
One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme…
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 prescribed orientation at the boundary of the domain. We obtain…
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 Theorem is concerned with the existence of a time-periodic…
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 the existence of solutions to this system which…
In this paper, a class of systems of pseudo-parabolic PDEs is considered. These systems (S)$_\varepsilon$ are derived as a pseudo-parabolic dissipation system of Kobayashi--Warren--Carter energy, proposed by [Kobayashi et al., Physica D,…
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 grain boundary motion. This model suffers from two key…
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 boundary motion, proposed by [Kobayashi et al, Physica D, 140,…
This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling, the limit system is formally derived when the interface…
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 the parabolic KWC system. However, such results have not…
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. In the original KWC system, the results of uniqueness have…
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 a phase-field model of grain boundary motion, proposed in…
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 focus is on problems in dimensions less than equal to 4. The…
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system,…
The microstructure evolution due to thermomechanical treatment of metals can largely be described by viscoplastic deformation, nucleation and grain growth. These processes take place over different length and time scales which present…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…
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 existence of solutions to the $L^2$-gradient descent flow of the…
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 that the equation for the crystalline orientation angle is…
We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…