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

The paper investigates the stability of exponential attractors for a family of semilinear wave equations with gentle dissipation: utt−Δu+γ(−Δ)αut+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 Aexpα and show their stability on the dissipative exponent α.