On basis property of a hyperbolic system with dynamic boundary condition

Abstract

This paper addresses the basis property of a linear hyperbolic system with dynamic boundary condition in one space variable whose general form was first studied in [15]. It is shown that under a regularity assumption, the spectrum of the system displays a distribution on the complex plane similar to zeros of a sine-type function and the generalized eigenfunctions of the system constitute a Riesz basis for its root subspace. The state space thereby decomposes into a topological direct sum of the root subspace with another invariant subspace in which the associated semigroup is supperstable: that is to say, the semigroup is identical to zero after a finite time. As a consequence, the spectrum-determined growth condition is established.