On exponential decay rate of semigroup associated with second order linear differential equation in Hilbert space with strong damping operator
Никита Вячеславович Артамонов · arXiv (Cornell University) · 2011
We obtain estimate of the exponential decay rate of semigroup associated with second order linear differential equation $u"+Du'+Au=0$ in Hilbert space. We assume that $A$ is a selfadjoint positive definite operator, $D$ is an accretive sectorial operator and $\Ree D\geqδA$, $δ>0$. We obtain a location of the spectrum of a pencil associated with linear differential equation.