On spectral and fractional powers of damped wave equations

Abstract

<p style='text-indent:20px;'>In this paper we explore the theory of fractional powers of positive operators, more precisely, we use the Balakrishnan formula to obtain parabolic approximations of (damped) wave equations in bounded smooth domains in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>. We also explicitly calculate the fractional powers of wave operators in terms of the fractional Laplacian in bounded smooth domains and characterize the spectrum of these operators.</p>