Zero-Dissipation Limit for Nonlinear Waves

Jerry L. Bona; Jiahong Wu

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 275-301
  • ISSN: 0764-583X

Abstract

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Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established.

How to cite

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Bona, Jerry L., and Wu, Jiahong. "Zero-Dissipation Limit for Nonlinear Waves." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 275-301. <http://eudml.org/doc/197459>.

@article{Bona2010,
abstract = { Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established. },
author = {Bona, Jerry L., Wu, Jiahong},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear; dispersive; dissipative; waves; inviscid limits; Korteweg-de Vries-Burgers type equations.; evolution equations; dispersion; dissipation; Korteweg-de Vries-Burgers equation; BBM-Burgers equation; zero dissipation limit; optimal convergence rates},
language = {eng},
month = {3},
number = {2},
pages = {275-301},
publisher = {EDP Sciences},
title = {Zero-Dissipation Limit for Nonlinear Waves},
url = {http://eudml.org/doc/197459},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Bona, Jerry L.
AU - Wu, Jiahong
TI - Zero-Dissipation Limit for Nonlinear Waves
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 275
EP - 301
AB - Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established.
LA - eng
KW - Nonlinear; dispersive; dissipative; waves; inviscid limits; Korteweg-de Vries-Burgers type equations.; evolution equations; dispersion; dissipation; Korteweg-de Vries-Burgers equation; BBM-Burgers equation; zero dissipation limit; optimal convergence rates
UR - http://eudml.org/doc/197459
ER -

References

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