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

• Main Authors: S. N. Antontsev, J. I. Díaz, H. B De Oliveira, Centro De Matemática
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2007
• Subjects: non-Newtonian fluids; glaciology; extinction in a finite time; finite speed of propagation; waiting; Ice Sheet
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.589.5451; http://w3.ualg.pt/~holivei/ADO-Porto-2007.pdf

time. 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. 1