Zero-Dissipation Limit for Nonlinear Waves
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.
2 Department of Mathematics, The University of Texas at Austin, RLM 8.100, C1200, Austin, Texas, 78712 USA.
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.
Mathematics Subject Classification: 35Q35 / 35Q53 / 76B03 / 76B15
Key words: Nonlinear / dispersive / dissipative / waves; inviscid limits; Korteweg-de Vries-Burgers type equations.
© EDP Sciences, SMAI, 2000