an:02126654
Zbl 1095.74011
Showalter, R. E.; Stefanelli, U.
Diffusion in poro-plastic media
EN
Math. Methods Appl. Sci. 27, No. 18, 2131-2151 (2004).
00111541
2004
j
74F10 74S05 74H20 74H25 35Q72 74C10 76R50
slightly compressible fluid; nonlinear evolution equation; existence; uniqueness
Summary: A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial-boundary value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto-viscoplastic type. The variational form of this problem in Hilbert space is a nonlinear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi-static momentum equation. The essential sufficient conditions for the well-posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid.