Event Detail

Event Type: 
Thursday, June 9, 2022 - 13:00 to 15:00
Kidder 274

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A fully saturated poroelastic medium is confined by the sides of a cylinder, and the regions below and above the medium are filled with fluid at respective constant pressures. The filtration flow of fluid through the poroelastic medium and the small deformations of the medium are described by a quasi-static Biot system of partial differential equations. Our objective, in this dissertation, is to establish the existence-uniqueness of a solution to this system for two different problems. We consider the Biot system for the case of, first, a linear poroelastic medium, and second, an inelastic (nonlinear elastic) medium, where the medium is fixed and sealed on the sides, free and in contact with the exterior fluid on the top and bottom, and displacement of the medium is unilaterally constrained on the top by a Signorini-type free boundary condition given by a variational inequality. Moreover, in both problems, we also include the degenerate case, where both fluid and the material of the medium are incompressible. The initial-boundary-value problem for this general system is formulated as a Cauchy problem in Hilbert space for a semilinear implicit evolution equation that is nonlinear in the time derivative, and it is shown to be well-posed with regularity of the solution dependent on the data.