Abstract
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.
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