Similarity solutions of an equation describing ice sheet dynamics
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Wiltshire, R. J. | |
| dc.date.accessioned | 2023-06-20T09:35:05Z | |
| dc.date.available | 2023-06-20T09:35:05Z | |
| dc.date.issued | 2006-04-15 | |
| dc.description.abstract | 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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15408 | |
| dc.identifier.doi | 10.1016/j.physd.2006.03.008 | |
| dc.identifier.issn | 0167-2789 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0167278906000856 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49966 | |
| dc.issue.number | 2 | |
| dc.journal.title | Physica D-Nonlinear Phenomena | |
| dc.language.iso | eng | |
| dc.page.final | 326 | |
| dc.page.initial | 319 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.95 | |
| dc.subject.keyword | nonlinear degenerate equations | |
| dc.subject.keyword | ice flow dynamics | |
| dc.subject.keyword | potential symmetries | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Similarity solutions of an equation describing ice sheet dynamics | |
| dc.type | journal article | |
| dc.volume.number | 216 | |
| dcterms.references | 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, http://www.mal.upc.es/cedya/cedya.html. J.I. Díaz, E. Schiavi, On a degenerate parabolic/hyperbolic system in glaciology giving rise to free boundary, Nonlinear Anal. 38 (1999) 649–673. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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