A Hyperbolic System in a One-Dimensional Network

Details A Hyperbolic System in a One-Dimensional Network A Hyperbolic System in a One-Dimensional Network

2002-09-09

arxiv.org/abs/math-ph/0209015v1

Physics

Mathematical Physics

35 pages, 3 figures

Scientific paper

We study a coupled system of Navier-Stokes equation and the equation of conservation of mass in a one-dimensional network. The system models the blood circulation in arterial networks. A special feature of the system is that the equations are coupled through boundary conditions at joints of the network. We prove the existence and uniqueness of the solution to the initial-boundary value problem, discuss the continuity of dependence of the solution and its derivatives on initial, boundary and forcing functions and their derivatives, develop a numerical scheme that generates discretized solutions, and prove the convergence of the scheme.

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