Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics

Cauchy problems for a second order linear differential operator equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{z}(t)+A_{0}z(t)+D\dot{z}(t)=0$$\end{document} in a Hilbert space H are studied. Equations of this kind arise for example in elasticity and hydrodynamics. It is assumed that A0 is a uniformly positive operator and that A0−1/2DA0−1/2 is a bounded accretive operator in H. The location of the spectrum of the corresponding semigroup generator is described and sufficient conditions for analyticity are given.