Potential Symmetry Properties of a Family of Equations Occuring in Ice Sheet Dynamics

• Published in: Pure and Applied Geophysics
• Main Authors: Díaz Díaz, Jesús Ildefonso, Wiltshire, R. J.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Birkhäuser 2008
• Subjects: Geología estratigráfica; Ice Sheet
• Online Access: https://eprints.ucm.es/id/eprint/15189/; https://eprints.ucm.es/id/eprint/15189/1/27.pdf; http://www.springerlink.com/content/t3414343k6x40421/; https://doi.org/10.1007/s00024-004-0393-4

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.