# American Institute of Mathematical Sciences

December  2014, 4(4): 521-554. doi: 10.3934/mcrf.2014.4.521

## Observability and controllability analysis of blood flow network

 1 Department of Mathematics, Tianjin University, Tianjin, 300072, China, China

Received  September 2013 Revised  January 2014 Published  September 2014

In this paper, we consider the initial-boundary value problem of a binary bifurcation model of the human arterial system. Firstly, we obtain a new pressure coupling condition at the junction based on the mass and energy conservation law. Then, we prove that the linearization system is interior well-posed and $L^2$ well-posed by using the semigroup theory of bounded linear operators. Further, by a complete spectral analysis for the system operator, we prove the completeness and Riesz basis property of the (generalized) eigenvectors of the system operator. Finally, we present some results on the boundary exact controllability and the boundary exact observability for the system.
Citation: Chun Zong, Gen Qi Xu. Observability and controllability analysis of blood flow network. Mathematical Control & Related Fields, 2014, 4 (4) : 521-554. doi: 10.3934/mcrf.2014.4.521
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