1. Introduction The classical Stefan problem is a model for phase transitions in solid-liquid systems and accounts for heat diiusion and exchange of latent heat in a homogeneous medium. The strong formulation of this model corresponds to a moving boundary problem involving a parabolic diiusion equation for each phase and a transmission condition prescribed at the interface separating the phases...

In this paper, a backstepping observer and an output feedback control law are designed for the stabilization of the one-phase Stefan Problem, which stands stand as an improvement of the recent full state feedback backstepping controller proposed in our previous contribution. The onephase Stefan Problem describes time evolution of a temperature profile in a solid-liquid material and its solid-li...

The level set method for capturing moving fronts was devised by Osher and Sethian in [3]. The goal is to compute and analyze the motion of an interface Γ that is moving according to its own geometries and/or the external physics of the underlying problem. The key idea behind this method is to implicitly represent the interface Γ as the zero level set of a smooth enough function φ, known as leve...

The evolution of the corrosion interface separating the uncorroded concrete part and the corroded part of a partially wet concrete wall of a pipe under the innuence of hydrogen sullde can be modelled by a moving boundary problem for three coupled one-dimensional diiusion equations. We show that the problem formulated via weak solutions is well-posed. The function describing the position of the ...

A moving-mesh finite-difference solution of a Lotka-Volterra competition-diffusion model theoretical ecology is described in which the competition sufficiently strong to spatially segregate two populations, leading two-phase problem with coupling condition at moving interface. mesh approach preserves identities species space and time, so that parameters always refer correct population. The impl...

The heat transfer problem of a moving heat source along the surface of a half space was studied analytically and numerically. For the 2D problem, the heat source was a strip moving source and for the 3D problem, the heat source was a square moving source. Analytical solutions are available only for adiabatic conditions as given by Carslaw and Jaeger [H.S. Carslaw, J.C. Jaeger, Conduction of Hea...

The physical model describing heat transfer and melting taking place during and after the interaction of a laser beam with a semi-infinite metal surface is based on the classical Stefan problem with appropriately chosen boundary conditions to reflect direct selective laser sintering of metals. A level set method for solving this problem is presented in this paper. From the results of these comp...

We study numerical approximations for a class of singularly perturbed problems of convection-diffusion type with a moving interior layer. In a domain (a segment) with a moving interface between two subdomains, we consider an initial boundary value problem for a singularly perturbed parabolic convection-diffusion equation. Convection fluxes on the subdomains are directed towards the interface. T...

We study numerical approximations for a class of singularly perturbed convection-diffusion type problems with a moving interior layer. In a domain (segment) with a moving interface between two subdomains, we consider an initial boundary value problem for a singularly perturbed parabolic convection-diffusion equation. Convection fluxes on the subdomains are directed towards the interface. The so...