On the stability of essential spectra of semigroups generated by one-dimensional hyperbolic systems

Abstract

<p style='text-indent:20px;'>This paper provides a new and systematic approach to stability properties of essential spectra or essential types for semigroups generated by hyperbolic systems in one space variable. In particular, we extend a previous theory by A.F. Neves et al <inline-formula><tex-math id="M1">\begin{document}$ \left[ \text{J. Funct. Anal 67(1986) 320-344}\right] $\end{document}</tex-math></inline-formula>. Our construction relies on a fine analysis of the difference of resolvent generators and on results on oscillatory integrals. Applications to stabilization of a Timoshenko beam system and to some discrete kinetic models are given.</p>