  We present a mixed dimensional model for a fractured poro-elasic medium
including contact mechanics. The fracture is a lower dimensional surface
embedded in a bulk poro-elastic matrix. The flow equation on the fracture is a
Darcy type model that follows the cubic law for permeability. The bulk
poro-elasticity is governed by fully dynamic Biot equations. The resulting
model is a mixed dimensional type where the fracture flow on a surface is
coupled to a bulk flow and geomechanics model. The particularity of the work
here is in considering fully dynamic Biot equation, that is, including an
inertia term, and the contact mechanics including friction for the fracture
surface. We prove the well-posedness of the continuous model.
