Mathematical Models in Dynamics of Non-Newtonian Fluids and in Glaciology

• Main Authors: Antontsev, S.N., Díaz Díaz, Jesús Ildefonso, Oliveira, H.B de
• Format: Book Part
• Language: English
• Published: APMTAC/FEUP 2007
• Subjects: Física; Ice Sheet
• Online Access: https://eprints.ucm.es/id/eprint/30284/; https://eprints.ucm.es/id/eprint/30284/1/170.pdf; http://www.mat.ucm.es/momat/Oporto_07_Antontsev_Diaz_Oliveira.pdf

This paper deals with the study of some qualitative properties of solutions of mathematical models in non-Newtonian isothermal fluid flows and in theoretical glaciology. In the first type of models, we consider the extinction in a finite time of the solutions by using a global energy method. We prove that this property holds for pseudo-plastic fluids or for the general class of Newtonian and dilatant fluids, assumed the presence of a dissipation term (which may have an anisotropic nature and can vanish in, at most, one spatial direction). In the case of the ice sheet model in Glaciology (with a formulation involving a quasi-linear degenerate equation similar to the ones arising in non-Newtonian flows), we analyze the behavior of the free boundary (given by the support of the height h of the ice sheet) for different cases and according to the values of the ablation function and the initial hight. We use here some other energy methods of a local nature and so completely different to the method used in the first part of the paper.