Erratum: long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term - III

Estimate (4.5) of proposition 2 of Milani (1991) is shown to be wrong, since it is not independent of ε as ε ↓ 0 as claimed. The correct estimate would be |▽ψ(t)| ≤ C(1 + εt)^-p{∥ψ₀∥_s(1) + ∥ψ₁∥_s(0)}, but this estimate is useless, since the uniform bound on the function (1 + εt)^p ∫₀^t (1 + ε(t - θ))^-p(1 + εθ)^-p dθ, which we would then have to consider in (4.12), is now of order 1/ε. This invalidates the proof of the main lemma, and hence of theorem 4.