Exponential decay of semigroups for second order non-selfadjoint linear differential equations

Abstract

The Cauchy problem for second order linear differential equation $u^{\prime \prime }(t)+D{u}^{\prime }(t)+Au(t)=0$ in Hilbert space $H$ with a sectorial operator $A$ and an accretive operator $D$ is studied. Sufficient conditions for exponential decay of the solutions are obtained.