Related papers: Uniqueness for solutions of the two-phase Stefan p…
Taking into account the recent works \cite{RoTaVe:2020} and \cite{Rys:2020}, we consider a phase-change problem for a one dimensional material with a non-local flux, expressed in terms of the Caputo derivative, which derives in a…
We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the initial data we introduce a novel "probabilistic" notion of…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
We study self-similar solutions of a multi-phase Stefan problem for a heat equation on the half-line $x>0$ with a constant initial data and with Dirichlet or Neumann boundary conditions. In the case of Dirichlet boundary condition we prove…
In this paper, a one-phase Stefan-type problem for a semi-infinite material which has as its main feature a variable latent heat that depends on the power of the position and the velocity of the moving boundary is studied. Exact solutions…
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…
We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback…
We prove locally in time the existence of a smooth solution for multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type. We establish also natural H\"{o}lder class for the boundary conditions…
A moment problem is presented for a class of signed measures which are termed pseudo-positive. Our main result says that for every pseudo-positive definite functional (subject to some reasonable restrictions) there exists a representing…
We address the problem of well-posedness for physical and minimal solutions to a probabilistic reformulation of the supercooled Stefan problem by investigating the sensitivity of these solutions to changes in the initial data. We show that…
We study existence, uniqueness and mass conservation of signed measure valued solutions of a class of stochastic evolution equations with respect to the Wiener sheet, including as particular cases the stochastic versions of the regularized…
One proves that the moving interface of a two-phase Stefan problem on $\ooo\subset\rr^d$, $d=1,2,3,$ is controllable at the end time $T$ by a Neumann boundary controller $u$. The phase-transition region is a mushy region $\{\sigma^u_t;\…
This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a…
We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.
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 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 establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent $C^2$ Dirichlet boundary data.
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
We argue that the celebrated Stefan condition on the moving interphase, accepted in mathematical physics up to now, can not be imposed if energy sources are spatially distributed in the volume. A method based on Tikhonov and Samarskii's…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…