Mathematical models in dynamics of non-Newtonian fluids and in glaciology

• Main Authors: S. N. Antontsev, J. I. Dı́az, H. B De Oliveira, Centro De Matemática
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2007
• Subjects: Ice Sheet
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.546.3239; http://w3.ualg.pt/~holivei/ABSTRACT-ADO-CMNE2007.pdf

In this talk, we give some generalization of the results presented in [1-3]. We study some qual-itative properties of the 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 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 formula-tion 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 talk.