Asymptotic models for viscoelastic one-dimensional blood flow

Abstract

We derive a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries. We prove local well-posedness of strong solutions in Sobolev spaces for general parameters and mean-zero periodic data. In the purely elastic BBM regime we further establish global existence and exponential decay for sufficiently small initial data. We also present a numerical study of the reduced model, including comparisons across different viscoelastic and amplitude regimes, and discuss the observed dynamics in connection with the continuation criterion.