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171.
Mauricio Cataldo Fabiola Ar��valo Patricio Mella 《Astrophysics and Space Science》2011,333(1):287-293
It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type scenarios are studied. We first consider the general case of a superposition of two ideal cosmic fluids, as well as the particular cases of non-interacting and interacting ones, by introducing a phenomenological coupling function q(t). For two-fluid cosmological scenarios there exist only cosmological scaling solutions, while for three-fluid configurations there exist not only cosmological scaling ones, but also more general solutions. In the case of triply interacting cosmic fluids we can have energy transfer from two fluids to a third one, or energy transfer from one cosmic fluid to the other two. It is shown that by requiring the positivity of energy densities there always is a matter component which violates the dominant energy condition in this kind of anisotropic cosmological scenarios. 相似文献
172.
In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known
in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based
on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used
to simplify the shallow water equations and contains as particular cases the porous medium equation and the p-Laplacian. Diverse
numerical schemes have been implemented to approximately solve the DSW equation and have been successfully applied as suitable
models to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis
has been carried out in order to study the properties of approximate solutions. In this study, we propose a numerical approach
as a means to understand some properties of solutions to the DSW equation and, thus, to provide conditions for which the use
of the DSW equation may be inappropriate from both the physical and the mathematical points of view, within the context of
shallow water modeling. For analysis purposes, we propose a numerical method based on the Galerkin method and we obtain a
priori error estimates between the approximate solutions and weak solutions to the DSW equation under physically consistent
assumptions. We also present some numerical experiments that provide relevant information about the accuracy of the proposed
numerical method to solve the DSW equation and the applicability of the DSW equation as a model to simulate observed quantities
in an experimental setting. 相似文献