| Summary: | CMNE CLAMCE 2007 Congresso Internacional em Métodos Numéricos em Engenharia, Porto, 13-15 junho 2007 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. “Centro de Matemática", Universidade da Beira Interior FCT (Portugal) Secretaria de Estado de Universidades e Investigación (Spain DGISGPI UCM/CM CMAF - University of Lisbon Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub
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