The ice flow behavior in the neighborhood of the grounding line. Non-Newtonian case

In this paper we address one of the problems that has attracted much interest in the glaciological scientific community which is the grounding line dynamics. The grounding line is the line where transition between ice attached to the solid ground and ice floating over the sea takes place. We analyze a mathematical model describing the ice flow near the grounding line where the ice is considered a non-Newtonian fluid. This generalizes the results obtained in [M.A. Fontelos, A.I. Muñoz, A free boundary problem in glaciology: The motion of grounding lines, Interfaces Free Bound. (9) (2007) 67–93] for the Newtonian case and allows us to consider a more realistic rheological model. We prove the existence and uniqueness (in a class to be defined) of weak solutions with moving grounding lines and zero contact angle and also determine the shape and asymptotic properties of the free boundary. Finally some finite element numerical simulations will illustrate the local and global behavior of the problem solutions.