Related papers: Well-posedness for a two-phase Stefan problem with…
We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem, physical experiments and heuristics indicate that the…
We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have finite velocities until the contact. Under these assumptions, we construct a smooth…
This paper deals with the exact controllability to the trajectories of the one--phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. It is assumed that the physical…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
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…
Recently, we have proposed a new free boundary problem representing the bread baking process in a hot oven. Unknown functions in this problem are the position of the evaporation front, the temperature field and the water content. For…
We study the nonlocal Stefan problem, where the phase transition is described by a nonlocal diffusion as well as the change of enthalpy functions. By using a stochastic optimization approach introduced for the local case, we construct…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
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,…
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,…
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…
We consider the one-phase Stefan problem describing the evolution of melting ice. On the one hand, we focus on understanding the evolution of the free boundary near isolated singular points, and we establish for the first time upper and…
The present article is dedicated to the forward and backward solution of a transient one-phase Stefan problem. In the forward problem, we compute the evolution of the initial domain for a Stefan problem where the melting temperature varies…
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…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium…
This paper develops an input-to-state stability (ISS) analysis of the Stefan problem with respect to an unknown heat loss. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a…
We analyze the operation of melting probes as a Stefan problem for the liquid/solid interface surrounding the probe. We assume that the liquid layer is thin and, therefore, amenable to analysis by lubrication theory. The resulting Stefan…
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…
In this chapter we consider different approximations for the one-dimensional one-phase Stefan problem corresponding to the fusion process of a semi-infinite material with a temperature boundary condition at the fixed face and non-linear…