Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 750185, 14 pages
http://dx.doi.org/10.1155/2013/750185
Research Article

Global Analysis of a Blood Flow Model with Artificial Boundaries

School of Mathematical Sciences, North-West University, Mafikeng 2735, South Africa

Received 3 June 2013; Accepted 4 August 2013

Academic Editors: S. He and K. Karamanos

Copyright © 2013 S. C. Oukouomi Noutchie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A theoretical model for blood flow in ramifying arteries was introduced and studied numerically (Quarteroni and Veneziani, 2003). A special experimental condition was considered on the artificial boundaries. In this paper, the aim is to analyze the well-posedness of this model, with the focus on the stilted boundary conditions. We use Brouwer’s fixed point theorem to show the existence of a solution to the stationary problem. For the evolutionary version, we use some energy estimates and Galerkin’s method to prove global existence, uniqueness, and stability of a weak solution.