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

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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{∥ψ0s(1) + ∥ψ1s(0)}, but this estimate is useless, since the uniform bound on the function (1 + εt)p0 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.

Original languageEnglish
Pages (from-to)367-368
Number of pages2
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number3
Publication statusPublished - Jan 1 1996


All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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