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

  • J. I. Díaz
  • R. J. Wiltshire
Part of the Pageoph Topical Volumes book series (PTV)


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 


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Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  • J. I. Díaz
    • 1
  • R. J. Wiltshire
    • 2
  1. 1.Departamento de Matemática Aplicada, Facultad de MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.The Division of Mathematics and StatisticsThe University of GlamorganPontypriddGreat Britain

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