Stability of exponential attractors for a family of semilinear wave equations with gentle dissipation

Abstract The paper investigates the stability of exponential attractors for a family of semilinear wave equations with gentle dissipation: u t t − Δ u + γ ( − Δ ) α u t + f ( u ) = g ( x ) , with α ∈ ( 0 , 1 / 2 ) . (i) We propose a new criterion on the existence and stability of a family of exponential attractors depending on the perturbation parameters. (ii) By applying this criterion to the equations, we construct a family of exponential attractors A e x p α and show their stability on the dissipative exponent α .