The Stationary Stefan Problem with Convection Governed by a Non-linear Darcy's Law

摘要

We consider the bidimensional stationary Stefan problem with convection. The problem is governed by a coupled system involving a non-linear Darcy's 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 fixed point principle.