We provide perturbative estimates for the one-phase Stefan free boundary problem and obtain regularity of flat boundaries via a linearization technique in spirit elliptic counterpart established De Silva (IFB 13, 223–238, 2011).

We introduce and discuss the Homotopy perturbation method, the Adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. Then, we give an example of the stefan problem with  kinetics and solve it by these methods.

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

A model for species diffusion is presented, with evaporation at a moving free boundary. The resulting problem resembles a one-phase Stefan problem with superheating, but the usual Stefan condition at the moving boundary is replaced by a version which, in the classical setting, would violate conservation of energy. In the fast evaporation limit, however, the problem reduces to a classical nonlin...

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...