Free boundary problems arising in the freezing of soils in a bounded region. II. Analytical treatment of the nonlinear parabolic free boundary problem

Abstract

This paper treats the parabolic free boundary problem which was stated in Part I and referred to as Problem I. Based upon potential theoretic arguments, we prove existence, uniqueness, and continuous dependence on the initial and boundary data of solutions to the problem. Along with these results, explicit expressions for the densities, the specific heats, and the thermal conductivities as functions of time and local coordinates in their respective phases, which fit our analysis, are also obtained.