### Impacto

Díaz Díaz, Jesús Ildefonso and Muñoz Montalvo, Ana Isabel and Schiavi, Emanuele
(2007)
*Existence of weak solutions to a system of nonlinear partial differential equations modelling ice streams.*
Nonlinear Analysis: Real World Applications, 8
(1).
pp. 267-287.
ISSN 1468-1218

PDF
Restringido a Repository staff only hasta 31 December 2020. 430kB |

Official URL: http://www.sciencedirect.com/science/article/pii/S1468121805001185

## Abstract

This paper deals with the mathematical analysis of a nonlinear system of three differential equations of mixed type. It describes the generation of fast ice streams in ice sheets flowing along soft and deformable beds. The system involves a nonlinear parabolic PDE with a multivalued. term in order to deal properly with a free boundary which is naturally associated to the problem of determining the basal water flux in a drainage system. The other two equations in the system are an ODE with a nonlocal (integral) term for the ice thickness, which accounts for mass conservation and a first order PDE describing the ice velocity of the system. We first consider an iterative decoupling procedure to the system equations to obtain the existence and uniqueness of solutions for the uncoupled problems. Then we prove the convergence of the iterative decoupling scheme to a bounded weak solution for the original system.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | surges; ice sheet models; nonlinear partial differential equations system of mixed type; free boundaries |

Subjects: | Sciences > Mathematics > Differential equations |

ID Code: | 15268 |

References: | H.W. Alt, S. Luckhaus, Quasilinear elliptic–parabolic differential equations, Math. Z. 183 (1993) 311–341. P. Benilan, Equations d'evolution dans un espace de Banach quelconque et applications, Thése, Orsay, 1972. P. Benilan, Evolution equations and accretive operators, Lecture Notes, University of Kentucky, 1972. P. Benilan, P. Wittbould, On mild and weak solutions of elliptic–parabolic problems, Adv. Differential Equations 1 (1996) 1053–1073. H. Brezis, Analyse Fonctionelle, Mason, Paris, 1983. N. Calvo, J. Durany, A.I. Muñoz, E. Schiavi, C. Vázquez, A coupled multivalued model for ice streams and its numerical simulations. IMA J. Appl. Math. 1–30 (2005), Advanced Access Published on May 17, 2005. J.I. Díaz, E. Schiavi, On a degenerate parabolic/hyperbolic system in glaciology giving rise to a free boundary, Nonlinear Anal. 38 (1999) 787–814. A.C. Fowler, Sliding with cavity formation, J. Glaciol. 33 (1987) 255–267. A.C. Fowler, Ice sheet surging and ice stream formation, Ann. Glaciol. 23 (1995) 68–73. A.C. Fowler, C. Johnson, Hydraulic runaway: a mechanism for thermally regulated surges of ice sheets, J. Glaciol. 41 (1995) 554–561. A.C. Fowler, E. Schiavi, A theory of ice sheet surges, J. Glaciol. 44 (146) (1998) 104–118. C. Johnson, The mathematical and numerical modelling of antartic ice streams, Ph.D. Thesis, University of Oxford, 1996. L.A. Lliboutry, Traité de Glaciologie, 1, Mason, Paris, 1964. A.I. Muñoz, Modelado, análisis y resolución numérica de un problema de obstáculo en glaciología, Ph.D. Thesis, Universidad Rey Juan Carlos, 2003. A.I. Muñoz, E. Schiavi, U. Kindelán, Non linear phenomena in glaciology: ice-surging and streaming, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A: Matemáticas. Racsam, vol. 95, Clave A, 2002. A.I. Muñoz, J.I. Tello, Uniqueness and collapse of solution for a mathematical model with nonlocal terms arising in glaciology, Math. Models Meth. Appl. Sci. 15 (4) (2005) 623–642. W.R. Peltier, S. Marshall, Coupled energy-balance/ice-sheet model simulations of the glacial cycle: a possible connection between terminations and terrigemous dust, J. Geophys. Res. 100 (1995) 14269–14289. R.L. Pfeffer, Dynamics of Climate, vol. 137, Pergamon Press, New York, 1960. J. Simon, Compacts sets in the space Lp (0,t;B) , Ann. Mat. Pura. Appl. 4 (CXLVI) (1987) 65–96. I. Vrabie, Compactness Methods for Nonlinear Evolutions, Pitman Monograph and Surveys in Pure and Applied Mathematics, vol. 32, 1987. J.L. Lions, Quelques méthodes de resolution des problémes aux limites non linéaires, Dunod, Paris, 1969. |

Deposited On: | 18 May 2012 09:09 |

Last Modified: | 06 Feb 2014 10:20 |

Repository Staff Only: item control page