Similarity solutions of an equation describing ice sheet dynamics

• Published in: Physica D: Nonlinear Phenomena
• Main Authors: Díaz Díaz, Jesús Ildefonso, Wiltshire, R. J.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Elsevier 2006
• Subjects: Ecuaciones diferenciales; Ice Sheet
• Online Access: https://eprints.ucm.es/id/eprint/15408/; https://eprints.ucm.es/id/eprint/15408/1/44.pdf; http://www.sciencedirect.com/science/article/pii/S0167278906000856; https://doi.org/10.1016/j.physd.2006.03.008

This paper focuses upon the derivation of the similarity solutions of a nonlinear equation associated with a free boundary problem arising in glaciology. We present a potential symmetry analysis of this second order nonlinear degenerate parabolic equation related to non-Newtonian ice sheet dynamics in the isothermal case. A full classical and also a non-classical symmetry analysis are presented. 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 of the free moving boundary in the presence of an accumulation-ablation function with realistic physical properties.