Related papers: Explicit solution for Stefan problem with latent h…
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 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…
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 +…
We study a two-phase modified Stefan problem modeling solid combustion and nonequilibrium phase transition. The problem is known to exhibit a variety of non-trivial dynamical scenarios. We develop a priori estimates and establish…
The (1+1)-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied by means of the classical Lie symmetry method. All possible Lie operators of the nonlinear heat equation, which…
The classical Stefan problem, concerning mere heat-transfer during solid-liquid phase transition, is here enhanced towards mechanical effects. The Eulerian description at large displacements is used with convective and Zaremba-Jaumann…
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…
A mathematical model for a one-phase change problem (particularly a Stefan problem) with a memory flux, is obtained. The hypothesis that the weighted sum of fluxes back in time is proportional to the gradient of temperature is considered.…
We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary…
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…
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…
Similarity solutions for the two-phase Rubinstein binary-alloy solidification problem in a semi-infinite material are developed. These new explicit solutions are obtained by considering two cases: a heat flux or a convective boundary…
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 continuous velocities until the moment of contact. Under these assumptions, we…
This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…
We study the existence and uniqueness of a solution to a linear stationary convection-diffusion equation stated in an infinite cylinder, Neumann boundary condition being imposed on the boundary. We assume that the cylinder is a junction of…
We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show that starting from arbitrary initial data, solution orbits…
We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently…
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 Stefan problem is reduced as the singular limit of phase-field equations. These equations are for temperature $u$ and the phase-field $\varphi$, consists of a heat equation: $$ u_t+\ell\varphi_t=\Delta u, $$ and a…
We construct examples for the one-phase Stefan problem which show that $\alpha$-concavity of the solution is in general not preserved in time, for $0 \le \alpha <1/2$. In particular, this shows that, in contrast to the case of the heat…