Related papers: The Nonlocal Stefan Problem via a Martingale Trans…
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…
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…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
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 nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order. This space-fractional equation admits an explicit, nonnegative,…
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 supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of systemic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the…
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…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…
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…
In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…
In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evolution of the density of sell and buy orders is the Heat…
Most heat transfer models for bulk crystal growth rely on the classical Stefan formulation to evaluate interface motion during phase change. However, when the interface is non-smooth the use of the classical Stefan formulation may lead to…
We study a class of one-dimensional interacting particle systems with random boundaries as a microscopic model for Stefan's melting and freezing problem. We prove that under diffusive rescaling these particle systems exhibit a hydrodynamic…
In this paper, we present a splitting algorithm to solve multicomponent transport models. These models are related to plasma simulations, in which we consider the local thermodynamic equilibrium and weakly ionised plasma-mixture models that…
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 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…
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly…
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…