Related papers: The Stefan problem and concavity
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 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 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…
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…
We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
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…
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 fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense. Then an equivalence with other two fractional Stefan problems (the first…
We show that the porous medium equation does not in general preserve $\alpha$-concavity of the pressure for $0\le\alpha<1/2$ or $1/2<\alpha\le 1$. In particular, this resolves an open problem of V\'azquez on whether concavity of pressure is…
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 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…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
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…
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…
In this paper a one-phase Stefan problem with size-dependent thermal conductivity is analysed. Approximate solutions to the problem are found via perturbation and numerical methods, and compared to the Neumann solution for the equivalent…
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…
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…
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 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…
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…