An existence theorem for a parabolic free boundary problem
Russell C. Thompson, Wolfgang L. Walter · Differential and Integral Equations · 1992
In this paper, the existence of a (classical) solution to a diffusion process with free boundary is obtained by applying Rothe's method (method of lines).A collection of semidiscrete approximate problems is obtained by discretizing the partial differential equations with respect to the time variable.A sequence of approximate solutions to the diffusion process is constructed from this collection of semi-discrete problems by interpolation between the lines in the grid.This sequence is then shown to converge to a solution to the free boundary problem.