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

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Antontsev, S.N. and Díaz Díaz, Jesús Ildefonso and Oliveira, H.B de (2007) Mathematical Models in Dynamics of Non-Newtonian Fluids and in Glaciology. In Métodos Numéricos e Computacionais em Engenharia. APMTAC/FEUP, Porto. ISBN 978-972-8953-16-4

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Official URL: http://www.mat.ucm.es/momat/Oporto_07_Antontsev_Diaz_Oliveira.pdf



Abstract

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.


Item Type:Book Section
Additional Information:

CMNE CLAMCE 2007
Congresso Internacional em Métodos Numéricos em Engenharia, Porto, 13-15 junho 2007

Uncontrolled Keywords:Non-Newtonian fluids; glaciology; extinction in a finite time; finite speed of propagation; waiting time.
Subjects:Sciences > Physics
ID Code:30284
Deposited On:22 May 2015 07:54
Last Modified:12 Dec 2018 15:07

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