Initial-boundary-value problem of hyperbolic equations for blood flow in a vessel

In this paper, we study an initial-boundary-value problem of a system of hyperbolic, partial-differential equations that models blood flow in a vessel. The one-spatial-dimensional model assumes that blood flow in the vessel is an incompressible, homogeneous, Newtonian fluid which has a small Womersley number. Boundary conditions with either the pressure or the flow rate at each end of the vessel are considered, and the existence of the global solution is obtained using a form of Glimm's finite-difference scheme.