We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

We consider a new Stefan-type problem for the classical heat equation with latent and phase-change temperature depending of variable time. prove equivalence this Stefan class boundary value problems nonlinear canonical evolution involving source term two free boundaries. This is obtained by applying reduction to Burgers reciprocal-type transformations. Moreover, particular case, we obtain uniqu...