An existence theorem for a parabolic free boundary problem (Q1198667)

The authors consider the one-dimensional heat conduction equation with nonlinear source function. They apply Rothe's method and, relying on earlier work, improve a priori estimates on the semidiscrete solution and the position of the free boundary. Interpolating linearly between time levels, a Lipschitz continuous function is obtained which is shown to converge to a weak solution of the original problem. This solution turns out to be classical, unique, and to depend continuously on the data.