Macro- and microsimulations for a sublimation growth of SiC single crystals.
Mathematical and computational aspects of solidification of pure substances.
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.
Mean curvature properties for -Laplace phase transitions
This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of -Laplacian type and a double well potential with suitable growth conditions. We prove that level sets of solutions of possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.
Method of straight lines for a Bingham problem as a model for the flow of waxy crude oils.
Mixed hybrid finite element scheme for Stefan problem with prescribed convection.
Modelling of free boundary problems for phase change with diffuse interfaces.
Modelling of the Czochralski flow.
Models for phase separation and their mathematics.
Modulational instability stabilization via complex Whitham deformations: Nonlinear Schrödinger equation
Motion of spirals by crystalline curvature
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Motion planning for a nonlinear Stefan problem
In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity....
Motion Planning for a nonlinear Stefan Problem
In this paper we consider a free boundary problem for a nonlinear parabolic partial differential equation. In particular, we are concerned with the inverse problem, which means we know the behavior of the free boundary a priori and would like a solution, e.g. a convergent series, in order to determine what the trajectories of the system should be for steady-state to steady-state boundary control. In this paper we combine two issues: the free boundary (Stefan) problem with a quadratic nonlinearity....
Multigrid solution of a two-phase Stefan problem with prescribed convection