Potential Symmetry Properties of a Family of Equations Occuring in Ice Sheet Dynamics
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 rela...
| Published in: | Pure and Applied Geophysics |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Birkhäuser
2008
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| Subjects: | |
| Online Access: | https://eprints.ucm.es/id/eprint/15189/ https://eprints.ucm.es/id/eprint/15189/1/27.pdf http://www.springerlink.com/content/t3414343k6x40421/ https://doi.org/10.1007/s00024-004-0393-4 |
| Summary: | 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. |
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