Related papers: Regularity for solutions of the two-phase Stefan p…
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…
We establish the local continuity of locally bounded weak solutions (temperatures) to the doubly singular parabolic equation modeling the phase transition of a material: \[ \partial_t \beta(u)-\Delta_p u\ni 0\quad\text{ for…
The two-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, composed…
A two-phase solidification process for a one-dimensional semi-infinite material is considered. It is assumed that it is ensued from a constant bulk temperature present in the vicinity of the fixed boundary, which it is modelled through a…
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…
We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and…
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…
Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of…
In this article we study a mathematical model of the heat transfer in semi infinite material with a variable cross section, when the radial component of the temperature gradient can be neglected in comparison with the axial component is…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
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…
We study the existence and properties of solutions and free boundaries of the one-phase Stefan problem with fractional diffusion posed in $\mathbb{R}^N$. In terms of the enthalpy $h(x,t)$, the evolution equation reads $\partial_t…
Recently it was obtained in [Tarzia, Thermal Sci. 21A (2017) 1-11] for the classical two-phase Lam\'e-Clapeyron-Stefan problem an equivalence between the temperature and convective boundary conditions at the fixed face under a certain…
We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…
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…
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…
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,…
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 +…
This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial…