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November  2001, 1(4): 403-420. doi: 10.3934/dcdsb.2001.1.403

Partially saturated flow in a poroelastic medium

R.E. Showalter 1, and  Ning Su 2,

1. 

Texas Institute for Computational and Applied Mathematics, Department of Mathematics, University of Texas at Austin, Austin, TX 78712, United States
2. 

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received  April 2001 Revised  July 2001 Published  September 2001

The formulation and existence theory is presented for a system modeling diffusion of a slightly compressible fluid through a partially saturated poroelastic medium. Nonlinear effects of density, saturation, porosity and permeability variations with pressure are included, and the seepage surface is determined by a variational inequality on the boundary.
Keywords: Poroelasticity, maximal monotone operator, partially saturated, deformable porous medium, consolidation, quasi-static, elliptic-parabolic system..
Mathematics Subject Classification: Primary: 76S05, 74F10; Secondary: 47J35, 35Q35,35K6.
Citation: R.E. Showalter, Ning Su. Partially saturated flow in a poroelastic medium. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 403-420. doi: 10.3934/dcdsb.2001.1.403
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