Asymptotics in shallow water waves

Robert McOwen; Peter Topalov

doi:10.3934/dcds.2015.35.3103

Article Contents

2015, Volume 35, Issue 7: 3103-3131. Doi: 10.3934/dcds.2015.35.3103

This issue Previous Article Multiple solutions to elliptic inclusions via critical point theory on closed convex sets Next Article Variational analysis of semilinear plate equation with free boundary conditions

Asymptotics in shallow water waves

Robert McOwen^1, and
Peter Topalov^1,

1.
Northeastern University, 360 Huntington Avenue, Boston, MA 02115

Received: August 2014

Revised: September 2014

Published: May 2017

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Abstract

In this paper we consider the initial value problem for a family of shallow water equations on the line $\mathbb{R}$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as $x\to\pm\infty$ and prove their invariance with respect to the solution map.

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Mathematics Subject Classification: 35Q35, 37K65, 35Q53, 37K10.

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