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Stationary expansion shocks for a regularized Boussinesq system

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posted on 18.08.2017 by Gennady El, M.A. Hoefer, Michael Shearer
Stationary expansion shocks have been recently identified as a new type of solution to hyperbolic conservation laws regularized by non-local dispersive terms that naturally arise in shallow-water theory. These expansion shocks were studied in [1] for the Benjamin-Bona-Mahony equation using matched asymptotic expansions. In this paper, we extend the analysis of [1] to the regularized Boussinesq system by using Riemann invariants of the underlying dispersionless shallow water equations. The extension for a system is non-trivial, requiring a combination of small amplitude, long-wave expansions with high order matched asymptotics. The constructed asymptotic solution is shown to be in excellent agreement with accurate numerical simulations of the Boussinesq system for a range of appropriately smoothed Riemann data.

Funding

The research of MS and MH is supported by National Science Foundation grants DMS-1517291 and CAREER DMS-1255422, respectively.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Studies in Applied Mathematics

Citation

EL, G.A., HOEFER, M.A. and SHEARER, M., 2018. Stationary expansion shocks for a regularized Boussinesq system. Studies in Applied Mathematics, 14(1), pp. 27-47.

Publisher

© Wiley

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

07/08/2017

Publication date

2017-09-14

Notes

This is the peer reviewed version of the following article: EL, G.A., HOEFER, M.A. and SHEARER, M., 2018. Stationary expansion shocks for a regularized Boussinesq system. Studies in Applied Mathematics, 14(1), pp. 27-47, which has been published in final form at https://doi.org/10.1111/sapm.12191. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

ISSN

0022-2526

eISSN

1467-9590

Language

en

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