In this paper we are interested in the Dirichlet problem of a hyperbolic-parabolic degenerate equation. Thanks to a global entropic formulation in the sense of F. Otto, we propose a result of existence and uniqueness of the entropic measure valued solution and of the entropic weak solution in the space DM.
In this paper we propose the study of a first-order non-linear hyperbolic equation in a bounded domain. We give a result of existence and uniqueness of the entropic measure-valued solution and of the entropic weak solution; for some general assumptions on the data.
On expose les difficultés d’ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l’Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d’unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d’un problème inverse posé par l’étude stratigraphique d’une colonne monolithologique.
En este artículo se estudia el análisis matemático de una ley de conservación que no es clásica. El modelo describe procesos estatigráficos en Geología y tiene en cuenta una condición de tasa de erosión limitada. En primer lugar se presentan el modelo físico y la formulación matemática (posiblemente nueva). Tras enunciar la definición solución se presentan las herramientas que permiten probar la existencia de soluciones.
On expose les difficultés d'ordre mathématique que posent des modèles récents de sédimentation-érosion de bassins élaborés par l'Institut Français du Pétrole et fondés sur la prise en compte de diverses contraintes d'unilatéralité. On présente quelques résultats partiels théoriques et des directions de recherche pour la résolution d'un problème inverse posé par l'étude stratigraphique d'une colonne monolithologique.
This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type , where is the maximal monotonous graph of the Heaviside function and is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the rate constraint in the conservation law, with a unilateral...
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy's law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
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