28 citations · 46 across the 12 of their papers we have counts for
12 papers
Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior
Yekaterina Epshteyn, Chang Liu, Chun Liu +1
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameter…
On the uniqueness of linear convection--diffusion equations with integral boundary conditions
Chiun-Chang Lee, Masashi Mizuno, Sang-Hyuck Moon
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary condi…
Local well-posedness of a nonlinear Fokker-Planck model
Yekaterina Epshteyn, Chang Liu, Chun Liu +1
Noise or fluctuations play an important role in the modeling and understanding of the behavior of various complex systems in nature. Fokker-Planck equations are powerful mathematic…
Long time behavior for a curvature flow of networks related to grain bundary motion with the effect of lattice misorientations
Takashi Kagaya, Masashi Mizuno, Keisuke Takasao
The mathematical model of grain boundary motion, including lattice misorientations' effect, is considered. When time-dependent lattice misorientations are state variables of the su…
A stochastic model of grain boundary dynamics: A Fokker-Planck perspective
Yekaterina Epshteyn, Chun Liu, Masashi Mizuno
Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orient…
Grain Growth and the Effect of Different Time Scales
Katayun Barmak, Anastasia Dunca, Yekaterina Epshteyn +2
Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a cruci…
A curve shortening equation with time-dependent mobility related to grain boundary motions
Masashi Mizuno, Keisuke Takasao
A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation p…
Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag
Yekaterina Epshteyn, Chun Liu, Masashi Mizuno
Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play an esse…
Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag
Yekaterina Epshteyn, Chun Liu, Masashi Mizuno
Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and con…
Gradient estimates for mean curvature flow with Neumann boundary conditions
Masashi Mizuno, Keisuke Takasao
We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the mean curvature flow. As an appli…
Convergence of the Allen-Cahn equation with Neumann boundary conditions
Masashi Mizuno, Yoshihiro Tonegawa
We study a singular limit problem of the Allen-Cahn equation with Neumann boundary conditions and general initial data of uniformly bounded energy. We prove that the time-parametri…
Hölder estimates for solutions of the Cauchy problem for the porous medium equation with external forces
Masashi Mizuno
We study the interior Hölder regularity problem for weak solutions of the porous medium equation with external forces. Since the porous medium equation is the typical example of de…