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The Korteweg-de Vries equation with small dispersion: Higher order Lax- Levermore theory. (English) Zbl 0705.35125
The aim of the author is to give an asymptotic analysis of the solution to the initial value problem for the KdV equation: \[ u_ t=\sigma uu_ x+\epsilon^ 2u_{xxx}=0 \] (with the small parameter \(\epsilon\)), \(\epsilon\to 0.\)
From this analysis, he deduces the nature of the oscillations, near shocks, of the equation \(u_ t+\sigma uu_ x=0\) (i.e. without \(\epsilon\)).
Reviewer: M.Derridj

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B25 Singular perturbations in context of PDEs
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