On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics

被引:49
作者
Calvo, N
Díaz, JI
Durany, J
Schiavi, E
Vázquez, C
机构
[1] Univ Vigo, Dept Matemat Aplicada, ETSI Telecomunicac, Vigo 36280, Spain
[2] Univ Complutense Madrid, Fac Matemat, Dept Matemat Aplicada, E-28040 Madrid, Spain
[3] Univ Rey Juan Carlos, ESCET, Dept Ciencias Expt & Ingn, E-28933 Madrid, Spain
[4] Univ A Coruna, Fac Informat, Dept Matemat, Coruna 15071 A, Spain
关键词
ice sheet models; nonlinear degenerate equations; free boundaries; weak solutions; finite elements; duality methods;
D O I
10.1137/S0036139901385345
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper deals with the weak formulation of a free ( moving) boundary problem arising in theoretical glaciology. Considering shallow ice sheet flow, we present the mathematical analysis and the numerical solution of the second order nonlinear degenerate parabolic equation modelling, in the isothermal case, the ice sheet non-Newtonian dynamics. An obstacle problem is then deduced and analyzed. The existence of a free boundary generated by the support of the solution is proved and its location and evolution are qualitatively described by using a comparison principle and an energy method. Then the solutions are numerically computed with a method of characteristics and a duality algorithm to deal with the resulting variational inequalities. The weak framework we introduce and its analysis (both qualitative and numerical) are not restricted to the simple physics of the ice sheet model we consider nor to the model dimension; they can be successfully applied to more realistic and sophisticated models related to other geophysical settings.
引用
收藏
页码:683 / 707
页数:25
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