A free moving boundary problem for the till layer below large ice sheets

We formulate a free moving boundary problem for the till (i.e., soil + water) layer that may form below glaciers or large ice sheets and is thought to be responsible for their catastrophic advance when the water content makes such layers slippery against shear deformations. We indicate how the FMBP is formulated, specialize it to steady plane flow and deduce an ordinary differential equation which describes the distribution of the solid's volume fraction across the layer. This differential equation is second order and gives rise to a singular perturbation solution procedure. This problem can be analysed under the assumption that the fluid viscosity is a monotonic function of the solid's volume fraction. However, in this paper we prove that by choosing a constant fluid viscosity and vanishing thermodynamic pressure the emerging solid volume fraction turns out to be physically meaningless.