Stability for some wave equations with singular damping

This work investigates the stability for the wave equation with damping γ(t,x)(−Δx)α∂tu defined on a bounded domain Ω ⊂Rd,d≥1. The damping coefficient γ(t,x)≥0 may degenerate to zero at some (t,x)∈[τ,+∞)×Ω. In contrast to the classical geometric control condition (GCC), we give the integral control condition (ICC) which means γ only has a positive lower bound in the sense of integral.