Elementary Wave Interactions in Two‐Layer Blood Flow Model

ABSTRACT In this work, we consider the Riemann problem for a hyperbolic system of partial differential equations (PDEs) governing two‐layer blood flows through arteries. The characteristics of Riemann invariants lead us to employ a projection of the elementary curves onto the reduced phase plane. Furthermore, exploiting the properties of these elementary curves, we establish the solution of the associated Riemann problem in this phase plane. Moreover, we have provided a necessary and sufficient condition on Riemann data for the existence of a vacuum. Finally, we investigate all possible cases of wave interaction rigorously in the phase plane.