Behavior of Kreiss bounded $C_0$-semigroups on a Hilbert space

Abstract

Let $0<\alpha \le 1$. We prove that a $\alpha$-Kreiss bounded $C_0$ semigroup $(T_t{)}_{t\ge 0}$ on a Hilbert space has asymptotics $||T_t||=O(t^{\alpha }/\sqrt{log(t)})$. Then, we give an application to perturbed wave equation.

arXiv comment5 pages