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Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-phase coupling. In this work, we develop a physics-informed…
In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and…
Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
One dimensional Stefan problems for a semi-infinite material with temperature dependent thermal coefficients are considered. Existence and uniqueness of solution are obtained imposing a Dirichlet or a Robin type condition at fixed face…
We address the existence and uniqueness of the so-called modified error function that arises in the study of phase-change problems with specific heat and thermal conductivity given by linear functions of the material temperature. This…
A generalized Neumann solution for the two-phase fractional Lam\'e--Clapeyron--Stefan problem for a semi--infinite material with constant initial temperature and a particular heat flux condition at the fixed face is obtained, when a…
We study the one-dimensional one-phase Stefan problem for the heat equation with a nonlinear boundary condition. We show that all solutions fall into one of three distinct types: global-in-time solutions with exponential decay,…
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered.…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by…
The classical one-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition, such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain…
A one phase Stefan problem in nonlinear conduction is considered. The problem is shown to admit a unique solution for small times. An exact solution is obtained which is a travelling front moving with constant speed.
In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values…
The heat transfer model for a one-dimensional supercooled melt during the final stage of solidification is considered. The Stefan problem for the determination of the temperature distribution is solved under the condition that (i) the…
The non-local in space two-phase Stefan problem (a prototype in phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits a unique weak solution. This formulation makes Stefan…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan problem. The present result is an improvement of the recent full state feedback backstepping controller…
We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.