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2009, Volume 23, Issue 4: 1191-1204. Doi: 10.3934/dcds.2009.23.1191
This issue Previous Article Numerical investigation of a two-dimensional Boussinesq system Next Article A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation

On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain

  • 1.

    Department of Mathematics, University of Athens,15784 Zographou, and Institute of Applied and Computational Mathematics, FO.R.T.H., P.O. Box 1385, 71110 Heraklion

  • 2.

    UMR de Mathématiques, Université de Paris-Sud, Bâtiment 425, P.O. Box 91405, Orsay

Received:  May 2007
Revised:  September 2007
Published online:  November 2008
Abstract / Introduction Related Papers Cited by
    Abstract
  • We consider a Boussinesq system of BBM-BBM type in two space dimensions. This system approximates the three-dimensional Euler equations and consists of three coupled nonlinear dispersive wave equations that describe propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. We show that the initial-boundary value problem for this system, posed on a bounded smooth plane domain with homogeneous Dirichlet or Neumann or reflective (mixed) boundary conditions, is locally well-posed in $H^1$. After making some remarks on the temporal interval of validity of these models, we discretize the system by a standard Galerkin-finite element method and present the results of some numerical experiments aimed at simulating two-dimensional surface wave flows in complex plane domains with a variety of initial and boundary conditions.
    Mathematics Subject Classification: 35Q53, 76B15, 65M60.

    Citation:
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