On a Doubly Nonlinear Parabolic Obstacle Problem Modelling Ice Sheet Dynamics

This paper deals with the weak formulation of a free moving boundary problem arising in theoretical glaciology Considering shallow ice sheet ow we present the mathematical analysis and the numerical resolution of the second order nonlinear degenerate parabolic equation modelling in the isothermal case the ice sheet non newtoniandynamics An obstacle problem is then deduced and analysed The existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method Then the solutions are numerically computed with a method of characteristics and a duality algorithm to cope with the resulting variational inequalities The weak framework we introduce and its analysis both qualitative and numerical are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension They can be applied succesfully to more realistic and sophisticated models related to other geophysical settings