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 sheet 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 equation 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 speed of propagations of local disturbances from the initial ice-thickness is finite. We prove also that the solutions of this problem have the waiting-time local behavior. Key–Words: ice sheet dynamics, existence, uniqueness, finite speed of propagations, waiting time.