Results 1 
3 of
3
Diffusion in PoroElastic Media
 Jour. Math. Anal. Appl
, 1998
"... . Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of se ..."
Abstract

Cited by 10 (7 self)
 Add to MetaCart
. Existence, uniqueness and regularity theory is developed for a general initialboundaryvalue problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasistatic system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasistatic assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...
Singlephase Flow in Composite Poroelastic Media
 Math. Methods Appl. Sci
, 2002
"... . The mathematical formulation and analysis of the BarenblattBiot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluidsaturated doublediffusion model of fractured rock. The model includes various degenerate ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
. The mathematical formulation and analysis of the BarenblattBiot model of elastic deformation and laminar flow in a heterogeneous porous medium is discussed. This describes consolidation processes in a fluidsaturated doublediffusion model of fractured rock. The model includes various degenerate cases, such as incompressible constituents or totally fissured components, and it is extended to include boundary conditions arising from partially exposed pores. The quasistatic initialboundary problem is shown to have a unique weak solution, and this solution is strong when the data are smoother. 1. Introduction Any model of fluid flow through a deformable solid matrix must account for the coupling between the mechanical behavior of the matrix and the fluid dynamics. For example, compression of the medium leads to increased pore pressure, if the compression is fast relative to the fluid flow rate. Conversely, an increase in pore pressure induces a dilation of the matrix in response to t...
Partially Saturated Flow in a Composite Poroelastic Medium
 in Poromechanics II, Grenoble, 2002, J.L. Auriault et al (editors), Balkema
"... Preliminary Report.) The model formulation and existence theory is described for di#usion of a barotropic fluid through a partially saturated poroelastic composite medium consisting of two components. This includes the BarenblattBiot doubledi #usion model of elastic deformation and laminar flow ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Preliminary Report.) The model formulation and existence theory is described for di#usion of a barotropic fluid through a partially saturated poroelastic composite medium consisting of two components. This includes the BarenblattBiot doubledi #usion model of elastic deformation and laminar flow in a fissured medium, such as consolidation processes in a system of fissures distributed throughout a matrix of highly porous cells. Nonlinear e#ects of density, saturation, porosity and permeability variations with pressure are included, and the seepage surfaces are determined by variational inequalities on the boundary.