Asymptotic models for viscoelastic one-dimensional blood flow

TL;DR

This paper develops an asymptotic model for blood flow in viscoelastic arteries, proves well-posedness and decay properties, and provides numerical analysis across regimes.

Contribution

It introduces a new unidirectional asymptotic model for viscoelastic blood flow and establishes mathematical properties and numerical insights.

Findings

Proved local well-posedness in Sobolev spaces.

Established global existence and decay in the elastic regime.

Performed numerical comparisons across viscoelastic regimes.

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.