Di usion in poro - plastic media
نویسندگان
چکیده
A model is developed for the ow of a slightly compressible uid through a saturated inelastic porous medium. The initial-boundary-value problem is a system that consists of the di usion equation for the uid 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. The variational form of this problem in Hilbert space is a non-linear 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 uid, negligible porosity, or a quasi-static momentum equation. The essential su cient conditions for the well-posedness of the system consist of an ellipticity condition on the term for di usion of uid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright ? 2004 John Wiley & Sons, Ltd.
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