Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 1

Large time behavior of the zero dispersion limit of the fifth order KdV equation

Pages: 87 – 109

DOI: https://dx.doi.org/10.4310/DPDE.2007.v4.n1.a3

Authors

Virgil Pierce (Department of Mathematics, Ohio State University, Columbus, Ohio, U.S.A.)

Fei-Ran Tian (Department of Mathematics, Ohio State University, Columbus, Ohio, U.S.A.)

Abstract

We study the zero dispersion limit of the fifth order KdV equations when time is sufficiently large. In general, the weak limit may be described by an arbitrary odd number of hyperbolic equations. Unlike the KdV case, these are non-strictly hyperbolic equations. However, we show that the weak limit is governed by three hyperbolic equations in a domain in the space-time for all times bigger than a large time. Outside this domain, the weak limit satisfies a single hyperbolic equation.

Keywords

zero dispersion limit, KdV equation, weak limit

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 1 January 2007