A phase-change problem for an extended heat conduction model

The aim of this paper is the analysis of a free boundary value related to a generalized heat conduction model. The qualitative analysis proposed in this paper is developed also in view of the applications of suitable computational schemes to obtain quantitative results. A basic role is played by the fundamental solution of a third-order operator, explicitly determined in a previous paper. We first discuss a method to obtain the solutions to a moving boundary value problem for a third-order operator. Next, by using the properties of the function K, the free boundary value problem is reduced to a Volterra nonlinear system for which an existence and uniqueness result is given.