Hölder damping for fractional wave equations

Abstract

For fractional wave equations with low Hölder regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The energy decay rates depend explicitly on the Hölder regularity of the damping. In particular, we show damping functions with lower Hölder regularities that below a certain threshold give slower energy decay.

arXiv comment10 pages, 1 figure