Stability for some wave equations with singular damping.

This work investigates the stability for the wave equation with damping γ (t , x) (− Δ x) α ∂ t u defined on a bounded domain Ω ⊂ R d , 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. [ABSTRACT FROM AUTHOR]