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We obtain estimate of the exponential decay rate of semigroup associated withsecond order linear differential equation $u"+Du'+Au=0$ in Hilbert space. Weassume that $A$ is a selfadjoint positive definite operator, $D$ is anaccretive sectorial operator and $\Ree D\geq\delta A$, $\delta>0$. We obtain alocation of the spectrum of a pencil associated with linear differentialequation.

On exponential decay rate of semigroup associated with second order linear differential equation in Hilbert space with strong damping operator