Qualitative properties of the ice-thickness in a 3D model S.N. ANTONTSEV

Abstract: In this work we consider a 3D isothermal mathematical model for ice sheets flows over a horizontal bedrock. The model is derived from the mechanics and dynamics of ice sheets and experimental results carried out in Glaciology. The final formulation of the model gives rise to a degenerate quasi-linear elliptic-parabolic equa-tion for the ice-thickness function. Under appropriated initial and Dirichlet boundary conditions, we discuss the existence and uniqueness of weak solutions for this problem. Then, we prove that the local speed of propagations of disturbances from the initial ice-thickness is finite. We prove also that the solutions of this problem have the waiting-time local behavior. To establish these properties we use here a suitable local energy method. Key–Words: ice sheet dynamics, existence, uniqueness, finite speed of propagations, waiting time.