Stationary expansion shocks for a regularized Boussinesq system
journal contributionposted on 18.08.2017 by Gennady El, M.A. Hoefer, Michael Shearer
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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  for the Benjamin-Bona-Mahony equation using matched asymptotic expansions. In this paper, we extend the analysis of  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.
The research of MS and MH is supported by National Science Foundation grants DMS-1517291 and CAREER DMS-1255422, respectively.
- Mathematical Sciences