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Poro-Inelastic Filtration coupled to Stokes Flow

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MIMW03 - From the continuum to the tectonic: the magma/mantle dynamics of planet earth

Models of flow of fluid through saturated inelastic porous media are described. The initial-boundary-value problem consists of a nonlinear 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-visco-plastic type. Existence and uniqueness of a global strong solution follows from 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.

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