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Earth Sciences and Mathematics

Part of the series Pageoph Topical Volumes pp 1643-1661

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

  • J. I. DíazAffiliated withDepartamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid
  • , R. J. WiltshireAffiliated withThe Division of Mathematics and Statistics, The University of Glamorgan

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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.

Key words

Ice flow dynamics potential symmetries