Abstract
In this paper we derive some similarity solutions of a nonlinear equation associated with a free boundary problem arising in the shallow-water approximation in glaciology. In addition we present a classical potential symmetry analysis of this second-order nonlinear degenerate parabolic equation related to non-Newtonian ice sheet dynamics in the isothermal case. After obtaining a general result connecting the thickness function of the ice sheet and the solution of the nonlinear equation (without any unilateral formulation), a particular example of a similarity solution to a problem formulated with Cauchy boundary conditions is described. This allows us to obtain several qualitative properties on the free moving boundary in the presence of an accumulation-ablation function with realistic physical properties.
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Díaz, J.I., Wiltshire, R.J. Potential Symmetry Properties of a Family of Equations Occuring in Ice Sheet Dynamics. Pure appl. geophys. 165, 1643–1661 (2008). https://doi.org/10.1007/s00024-004-0393-4
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DOI: https://doi.org/10.1007/s00024-004-0393-4