Trace properties of certain damped linear elastic systems
David L. Russell · Evolution equations and control theory · 2013
We study the spectrum of a damped linear elastic system with discrete eigenvalues, showing the relationship between the sum of the real parts of the eigenvalues of the (generally unbounded) generator and the trace of the damping operator, assuming the latter to be a trace type operator.Some relationships between the sequence of eigenvectors and a corresponding orthonormal sequence, constructed by means of a variant of the Gram-Schmidt method, are also explored. A simple hybrid system is presented as an example of application.