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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Official URL: http://www.sciencedirect.com/science/article/pii/S0167278906000856

## 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 |
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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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