Related papers: On solutions of an ill-posed Stefan problem
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.
Solving the Stefan problem, also referred as the heat conduction problem with phase change, is a necessary step to solve phase change problems with convection. In this article, we are interested in using the Lattice Boltzmann Method (LBM)…
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 is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
In this article, we study the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation. This model contains the terms $\cal{D}_t^\alpha(u_t)$ and $\cal{D}_t^\alpha u $ (with $\alpha \in(0,1)$), where…
We review some fractional free boundary problems that were recently considered for modeling anomalous phase-transitions. All problems are of Stefan type and involve fractional derivatives in time according to Caputo's definition. We survey…
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 derive two weak formulations for the supercooled Stefan problem with transport noise on a half-line: one captures a continuously evolving system, while the other resolves blow-ups by allowing for jump discontinuities in the evolution of…
This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…
We study the supercooled Stefan problem in arbitrary dimensions. First, we study general solutions and their irregularities, showing generic fractal freezing and nucleation, based on a novel Markovian gluing principle. In contrast, we then…
We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension - also known as the Stefan problem with Gibbs-Thomson correction.
We study the regularity of the bounded self-similar solution to the one-phase Stefan problem with fractional diffusion posed on the whole line. In terms of the enthalpy $h(x,t)$, the evolution problem reads \[ \begin{cases} \partial_t h +…
Two fractional two-phase Stefan-like problems are considered by using Riemann-Liouville and Caputo derivatives of order $\alpha \in (0, 1)$ verifying that they coincide with the same classical Stefan problem at the limit case when…
We consider the problem of heat conduction with phase change, that is essential for permafrost modeling in Land Surface Models and Dynamic Global Vegetation Models. These models require minimal computational effort and an extremely robust…
This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…
In this paper, we derive a thermodynamically consistent non-isothermal diffuse interface model for phase transition and interface evolution involving heat transfer. This model is constructed by integrating concepts from classical…
The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study [16] attempted to reconstruct the unknown…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
We prove the global-time existence of weak solutions to the supercooled Stefan problem. Our result holds in general space dimensions and with a general class of initial data. In addition, our solution is maximal in the sense of a certain…
The computer simulation of quasistationary Stefan problem has been realized. Different representations of the Laplacian growth model are considered. The main attention has been paid for the interface dynamics represented by integro…