On the variational formulation of a transmission problem for the Biot equations
Robert Pertsch Gilbert, George C. Hsiao, Liwei Xu · Applicable Analysis · 2010
In this article, a variational formulation for the transmission problem of the fluid–bone interaction is formulated. The formulation is based on a modified Biot system of equations for the cancellous bone together with a boundary integral equation formulation of the pressure in the water. Existence and uniqueness for the weak solution of the interaction problem are established in appropriate Sobolev spaces.