### Abstract

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}{∥ψ_{0}∥_{s(1)} + ∥ψ_{1}∥_{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.

Original language | English |
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Pages (from-to) | 367-368 |

Number of pages | 2 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 27 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1996 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### Cite this

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**Erratum : long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term - III.** / Milani, Albert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Erratum

T2 - long time existence and singular perturbation results for quasilinear hyperbolic equations with small parameter and dissipation term - III

AU - Milani, Albert

PY - 1996/1/1

Y1 - 1996/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030214175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030214175&partnerID=8YFLogxK

U2 - 10.1016/0362-546X(95)00057-3

DO - 10.1016/0362-546X(95)00057-3

M3 - Article

AN - SCOPUS:0030214175

VL - 27

SP - 367

EP - 368

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 3

ER -