A self‐similar solution to time‐fractional Stefan problem

Exact solution of a Stefan problem in a nonhomogeneous cylinder

The exact solution is found for the Stefan problem of inwards freezing of a nonhomogeneous cylinder whose specific heat and latent heat depend upon the inverse square of the radial distance. The freezing time for the corresponding annular cylinder is found exactly. The validity of the pseudo-steady-state approximation for the solvable cylinder problem is verified explicitly. It is argued that t...

A Uniqueness Theorem for the Solution of a Stefan Problem

A Stochastic Stefan Problem

We consider a stochastic perturbation of the Stefan problem. The noise is Brownian in time and smoothly correlated in space. We prove existence and uniqueness and characterize the domain of existence.

Nonlinear Two-Phase Stefan Problem

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

Newton-Product Integration for a Stefan Problem with Kinetics

Stefan problem with kinetics is reduced to a system of nonlinear Volterra integral equations of second kind and Newton's method is applied to linearize it. Product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. An example is provided to illustrated the applicability of the method.