Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics (Q731313)

Cauchy problems for a second order linear differential operator equation \[ \ddot{z}(t)+A_{0}z(t)+D\dot{z}(t)=0 \] in a Hilbert space \(H\) are studied. Equations of this kind arise for example in elasticity and hydrodynamics. It is assumed that \(A _{0}\) is a uniformly positive operator and that \(A_0^{-1/2}DA_0^{-1/2}\) 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.