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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.

Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics