Expansion of solution in terms of generalized eigenfunctions for a hyperbolic system with static boundary condition

This paper studies a linear hyperbolic system with static boundary condition that was first studied in Neves et al. [J. Funct. Anal. 67(1986) 320–344]. It is shown that the spectrum of the system consists of zeros of a sine-type function and the generalized eigenfunctions of the system constitute a Riesz basis with parentheses for the root subspace. The state space thereby decomposes into topological direct sum of root subspace and another invariant subspace in which the associated semigroup is superstable: that is to say, the semigroup is identical to zero after a finite time period.