no. 2
Vertical compaction in a faulted sedimentary basin
ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 373-388.

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. The uniqueness proof, by Holmgren's method, leads to work out a linear, strongly coupled, system of partial differential equations and boundary conditions.

DOI : 10.1051/m2an:2003032
Classification : 35Q35, 76S05, 35J65
Mots clés : porous media, vertical compaction, sedimentary basins, fault lines modelling 
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     title = {Vertical compaction in a faulted sedimentary basin},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {373--388},
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Gagneux, Gérard; Masson, Roland; Plouvier-Debaigt, Anne; Vallet, Guy; Wolf, Sylvie. Vertical compaction in a faulted sedimentary basin. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 2, pp. 373-388. doi : 10.1051/m2an:2003032. http://www.numdam.org/articles/10.1051/m2an:2003032/

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