Complutense University Library

Similarity solutions of an equation describing ice sheet dynamics


Díaz Díaz, Jesús Ildefonso and Wiltshire, R. J. (2006) Similarity solutions of an equation describing ice sheet dynamics. Physica D-Nonlinear Phenomena, 216 (2). pp. 319-326. ISSN 0167-2789

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


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.

Item Type:Article
Uncontrolled Keywords:nonlinear degenerate equations; ice flow dynamics; potential symmetries
Subjects:Sciences > Mathematics > Differential equations
ID Code:15408

A.C. Fowler, Modelling ice sheet dynamics, Geophys. Astrophys. Fluid Dyn. 63 (1992) 29–65.

N. Calvo, J.I. Díaz, J. Durany, E. Schiavi, C. Vázquez, On a doubly nonlinear obstacle problem modelling ice sheet dynamics, SIAM J. Appl. Math. 29 (2) (2002) 683–707.

S.N. Antontsev, J.I. Díaz, S.I. Shmarev, Energy Methods for Free Boundary Problems, Birkhäuser, Boston, 2002.

W.S.B. Paterson, The Physics of Glaciers, Pergamon, Oxford, 1981.

G.W. Bluman, G.J. Reid, S. Kumei, New classes of symmetries for partial differential equations, J. Math. Phys. 29 (1988) 806.

G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.

G.W. Bluman, J.D. Cole, The general similarity solution of the heat equation, J. Math. Mech. 18 (1969) 1025–1042.

J. Carrillo, P. Wittbold, Uniqueness of renormalized solutions of degenerate elliptic–parabolic problems, J. Differential Equations 156 (1999) 93–121.

J.I. Díaz, S.I. Shmarev, A Lagrangian approach to level sets: Application to a free boundary problem in climatology (preprint).

J.I. Díaz, E. Schiavi, Tratamiento matematico de una ecuacion parabolica cuasilineal degenerada en Glaciologia, in: Electronic Proceedings of the XIV CEDYA-IV Congreso de Matemática Aplicada, Vic, Barcelona, 1995,

J.I. Díaz, E. Schiavi, On a degenerate parabolic/hyperbolic system in glaciology giving rise to free boundary, Nonlinear Anal. 38 (1999) 649–673.

Deposited On:29 May 2012 09:21
Last Modified:06 Feb 2014 10:24

Repository Staff Only: item control page