Díaz Díaz, Jesús IldefonsoWiltshire, R. J.2023-06-202023-06-202008-080033-455310.1007/s00024-004-0393-4https://hdl.handle.net/20.500.14352/49919In 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.engjournal articlehttp://www.springerlink.com/content/t3414343k6x40421/http://www.springerlink.com/restricted access551.32Ice flow dynamicspotential symmetriesGeología estratigráfica2506.19 Estratigrafía