A homogenized phase field model for phase transitions in porous media is considered. By making use of the method of formal asymptotic expansion with respect to the interface thickness, a sharp interface limit problem is derived. This limit problem turns out to be similar to the classical Stefan problem with surface tension and kinetic undercooling.

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...

This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...

We show that the quasi-stationary two-phase Stefan problem with surface tension has a unique smooth local solution. In addition we show that smooth solutions exist globally, provided that the initial interface is close to a sphere and no heat is supplied or withdrawn.

We construct and investigate local invariant manifolds for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions and study their attractivity properties. In a companion paper we have developed the corresponding solution theory. Examples for the class of systems considered are reaction–diffusion systems or phase field models with dynamical boundary co...