On the variational formulation of a transmission problem for the Biot equations

Abstract

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.

Keywords:

• Biot equations
• transmission problem
• Green's formula
• variational problem
• Gårding's inequality
• Sobolev spaces

AMS Subject Classifications::

• 35J05
• 35J20
• 35C15
• 65N38

Acknowledgement

This research was supported in part by the NSF through grant No. DMS-0920850.