Collision between weak shock waves for a two-layer blood flow model

This paper investigates the collision of two weak shocks of the Riemann problem for a two-layer blood flow model characterized by physiological parameter representative of arteries. The model considered vertical averages across each layer derived from the Euler equations of gas dynamics, which described a quasi-linear hyperbolic system of conservation laws. We explore the elementary waves, specifically the shock, rarefaction and contact discontinuity, using the method of characteristics and derive the curves in one parameter form. Moreover, the existence-uniqueness of the Riemann solution is proved locally, ensuring its compatibility with numerical simulations, for arbitrary data. Furthermore, we determine a necessary and sufficient condition for shock waves or rarefaction waves based on the initial data of the Riemann problem. At the end, the interaction of two weak shocks from the same family is analyzed explicitly.