<p style='text-indent:20px;'>We consider the problem of recovering initial condition in one-dimensional one-phase Stefan for heat equation from knowledge position melting point. We first recall some properties free boundary solution. Then we study uniqueness and stability inversion. The principal contribution paper is a new logarithmic type estimate that shows inversion may be severely il...

The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modiied Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A nite element method for discretization of the Stefan problem is...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

An approximation procedure for the identi cation 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 solidi cation surface in the Stefan problem. The analysis is based on Hilbert space methods and convex analysis techniques. Numerical results combining two...