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Zero-Dissipation Limit for Nonlinear Waves

Published online by Cambridge University Press:  15 April 2002

Jerry L. Bona  and
Jiahong Wu
Jerry L. Bona
Affiliation:
Department of Mathematics and the Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, RLM 8.100, C1200, Austin, Texas, 78712 USA.
Jiahong Wu
Affiliation:
Department of Mathematics, The University of Texas at Austin, RLM 8.100, C1200, Austin, Texas, 78712 USA.
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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.

Keywords

Nonlineardispersivedissipativewaves; inviscid limits; Korteweg-de Vries-Burgers type equations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 275 - 301
Copyright
© EDP Sciences, SMAI, 2000

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