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Title: Stationary expansion shocks for a regularized Boussinesq system
Authors: El, G.A.
Hoefer, M.A.
Shearer, Michael
Issue Date: 2017
Publisher: © Wiley
Citation: EL, G.A., HOEFER, M.A. and SHEARER, M., 2017. Stationary expansion shocks for a regularized Boussinesq system. Studies in Applied Mathematics, In Press.
Abstract: 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.
Description: This paper is closed access until 12 months after publication.
Sponsor: The research of MS and MH is supported by National Science Foundation grants DMS-1517291 and CAREER DMS-1255422, respectively.
Version: Accepted for publication
DOI: 10.1111/sapm.12191
URI: https://dspace.lboro.ac.uk/2134/26134
Publisher Link: https://doi.org/10.1111/sapm.12191
ISSN: 0022-2526
Appears in Collections:Closed Access (Maths)

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