On the investigation of a one-dimensional blood flow model in elastic arteries under symmetry analysis

Abstract

In this paper, we consider a one-dimensional model of blood flow along the compliant arteries. With the help of the invariant function, we construct and classify the optimal system of subalgebras. Next, we reduced the given system of partial differential equations (PDEs) to the system of ordinary differential equations (ODEs) for each subalgebra and subsequently solved them exactly. Further, we investigate the evolutionary behavior of the average blood flow velocity and the cross-sectional area of the arteries; under the influence of the physical parameter [Formula: see text] graphically. Furthermore, we construct nonlocally related PDEs for the given system of PDEs, consisting of inverse potential systems (IPS) and potential systems. Finally, we classify the nonlocal symmetries arising from the potential system and IPS.

Study of optimal subalgebras, invariant solutions, and conservation laws for a Verhulst biological population model

“…Shagolshem et al. presented the articles on the one‐dimensional blood flow model, 29,30 and a paper on the biological population model with Malthusian law 31 using Lie symmetry analysis.…”