Mathematical Analysis of a Stefan Problem with Dirichlet–Signorini Boundary Conditions Appearing in Polythermic Ice Sheet Modeling

In this paper, a Stefan problem from theoretical glaciology with Dirichlet– Signorini boundary conditions is analyzed. The existence of a weak solution for the nonlinear evolutive model is shown by using an implicit time discretization, an enthalpy regularization procedure, and a Galerkin-type method. The main goal has been to adapt the previous techniques to the specific boundary conditions of the problem.