The Riemann Problem for the Blood Flow Model with Body Force Term

Abstract

In this paper, we study the Riemann problem for the blood flow model with body force term. The Riemann solutions involve the rarefaction waves, the shock waves, and the collapsed state. Due to the effect of body force term, the solutions are not self‐similar. By a transformation, the system can be transformed into the nonreducible blood flow model. The existence of the simple wave solutions to the nonreducible blood flow model is obtained by the method of characteristic decomposition. All Riemann solutions are constructed for any given Riemann initial data. The simple wave and shock wave connected to two constant states on both sides are not straight lines, which are the key innovation and different from the results for the reducible system.