Similarity solutions of an equation describing ice sheet dynamics
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...
| Published in: | Physica D: Nonlinear Phenomena |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
Elsevier
2006
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| Subjects: | |
| Online Access: | https://eprints.ucm.es/id/eprint/15408/ https://eprints.ucm.es/id/eprint/15408/1/44.pdf http://www.sciencedirect.com/science/article/pii/S0167278906000856 https://doi.org/10.1016/j.physd.2006.03.008 |
| Summary: | 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. |
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