Equivalence between the energy decay of fractional damped Klein-Gordon equations and geometric conditions for damping coefficients

Kotaro Inami, Soichiro Suzuki

We consider damped $s$-fractional Klein--Gordon equations on ${\mathbb{R}}^d$, where $s$ denotes the order of the fractional Laplacian. In the one-dimensional case $d=1$, Green (20…