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

Abstract

We obtain estimate of the exponential decay rate of semigroup associated with second order linear differential equation $u"+D{u}^{\prime }+Au=0$ in Hilbert space. We assume that $A$ is a selfadjoint positive definite operator, $D$ is an accretive sectorial operator and $\Ree D\geqδA$, $\delta >0$. We obtain a location of the spectrum of a pencil associated with linear differential equation.