In this paper we consider stationary ice sheet modelled as a Stokes flow in a bounded two-dimensional domain. In particular, we study the behavior of the grounding line, where different boundary conditions meet: no-slip conditions for the grounded part and force balance conditions for the floating part whose shape is a priori undetermined. This yields a free boundary problem with mixed boundary conditions and a contact line, called "left grounding line" in the glaciological context, that might move along the solid substrate. We show that solutions with moving grounding lines and zero contact angle do exist and determine the shape and asymptotic properties of the free boundary.
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Marco Antonio Fontelos, Ana I. Muñoz, A free boundary problem in glaciology: The motion of grounding lines. Interfaces Free Bound. 9 (2007), no. 1, pp. 67–93DOI 10.4171/IFB/156