Generalized Lamé-Clapeyron solution for a one-phase source Stefan problem (Q1328478)

The authors derive self-similar solution of the one-phase one-dimensional Stefan problem with a source term of the type \(g(x,t)= \alpha t^{-1} \beta(x/2a t^{1/2})\), establishing necessary and sufficient conditions on the function \(\beta\) for the existence and for the uniqueness of such solutions. The quasi-steady case is also analyzed.