Mathematics

The quasi-static Biot system is a coupled system of parabolic and elliptic partial differential equations that describe the small deformations of and fluid flow through a fully saturated elastic and porous structure. Examples include subsurface flow of groundwater and blood flow through tissue. Our objective is to extend the existence-uniqueness-regularity theory for such systems to include problems with constraints on the displacement and friction at interfaces. Such contact problems are highly nonlinear and ubiquitous in the applications.