Abstract
This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11].
Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper.
It is shown that the associated linear system is the infinitesimal generator of a
{C_{0}}
-semigroup; its spectrum consists of zeros of a sine-type function, and its exponential system
{\{e^{\lambda_{n}t}\}_{n\geq 1}}
constitutes a Riesz basis in
{L^{2}[0,T]}
.
Furthermore, by the spectral analysis method, it is also shown that the linear system has a sequence of eigenvectors, which form a Riesz basis in Hilbert space, and hence the spectrum-determined growth condition is deduced.
Flatness based trajectory planning for a semi-linear hyperbolic system of first order p.d.e. modeling a tubular reactor
