In this paper we obtain a generalized Lamé-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.
J.-L. Menaldi and D. A. Tarzia, "Generalized Lame-Clapeyron solution for a one-phase source Stefan problem", Comp. Appl. Math., 12 (1993), pp. 123-142.