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Similarity solutions of an equation describing ice sheet dynamics

Díaz Díaz, Jesús Ildefonso and Wiltshire, R. J. (2006) Similarity solutions of an equation describing ice sheet dynamics. Physica D-Nonlinear Phenomena, 216 (2). pp. 319-326. ISSN 0167-2789

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:nonlinear degenerate equations; ice flow dynamics; potential symmetries
Subjects:Sciences > Mathematics > Differential equations
ID Code:15408
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Deposited On:29 May 2012 09:21
Last Modified:06 Feb 2014 10:24

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