Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 72, pp. 1-19.

Title: Non-autonomous approximations governed by the fractional powers
       of damped wave operators

Authors: Marcelo J. D. Nascimento, Flank D. M. Bezerra

Abstract:
 In this article we study non-autonomous approximations governed by the 
 fractional powers  of damped wave operators of order $\alpha \in (0,1)$ 
 subject to Dirichlet boundary  conditions in an $n$-dimensional bounded 
 domain with smooth boundary.  We give explicitly expressions for the 
 fractional powers of the wave operator, we compute their resolvent 
 operators and their eigenvalues. Moreover,  we study the convergence 
 as $\alpha\nearrow 1$ with rate $1-\alpha$.

Submitted January 24, 2019. Published May 17, 2019.
Math Subject Classifications: 35L05, 35B40.
Key Words: Non-autonomous damped wave equations; fractional powers; 
           rate of convergence; eigenvalues.