An approximation procedure for the identiication of a nonlinear boundary heat transfer function in a one phase Stefan problem is presented. Alternatively the problem can be viewed as constructing a feedback control law for the control of the solidiication surface in the Stefan problem. The analysis is based on Hilbert space methods and convex analysis techniques. Numerical results combining two...

We study a novel two–sided Stefan problem – motivated by the study of certain 2D interfaces – in which boundaries at both sides of the sample encroach into the bulk with rate equal to the boundary value of the gradient. Here the density is in [0, 1] and takes the two extreme values at the two free boundaries. It is noted that the problem is borderline ill–posed: densities in excess of unity lia...

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...