RT Journal Article
T1 On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics
A1 Díaz Díaz, Jesús Ildefonso
A1 Calvo, N.
A1 Durany, J.
A1 Schiavi, E.
A1 Vázquez, C.
AB 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.
PB Society for Industrial and Applied Mathematics
SN 0036-1399
YR 2002
FD 2002
LK https://hdl.handle.net/20.500.14352/57038
UL https://hdl.handle.net/20.500.14352/57038
LA eng
NO D.G.E.S
DS Docta Complutense
RD 11 abr 2025