Author(s)

Ranis Ibragimov¹, Nail Ibragimov^2,3, Pirooz Mohazzabi¹

¹Department of Mathematics and Physics, University of Wisconsin-Parkside, Kenosha, WI, USA.
²Center ALGA, Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, Karlskrona, Sweden.
³Laboratory, “Group Analysis of Mathematical Models in Natural and Engineering Sciences,” Ufa State Aviation Technical University, Ufa, Russia.

We examine governing equations that could be used to model a one-dimensional blood flow within a pulsating elastic artery that is represented by a tube of varying cross-section. The model is considered from two perspectives. The first represents a singular perturbation theory providing explicit approximate solutions to the model, and the second is based on group theoretical modeling that provides exact solutions in implicit form. The main goal is to compare these two approaches and lay out the advantages and disadvantages of each approach.

Blood Flow, Variable Density, Approximate, Invariant, Solution

Ibragimov, R. , Ibragimov, N. and Mohazzabi, P. (2017) Approximate and Invariant Solutions of a Mathematical Model Describing a Simple One-Dimensional Blood Flow of Variable Density. Journal of Applied Mathematics and Physics, 5, 1335-1354. doi: 10.4236/jamp.2017.56111.