Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Existence of solutions for a Boussinesq system on the half line and on a finite interval

Pages: 25 - 49, Volume 29, Issue 1, January 2011      doi:10.3934/dcds.2011.29.25

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Karine Adamy - Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, CNRS UMR 8628, 91405 Orsay, France (email)

Abstract: The initial boundary-value problem for a Boussinesq system is studied on the half line and on a finite interval. Global existence of weak solutions satisfying the boundary conditions is proven and uniqueness for solutions in a suitable class is studied. A proof of the persistence of finite regularity for solutions in the whole space is also presented.

Keywords:  Boussinesq systems, boundary value problems, hyperbolic systems, regularity of solutions.
Mathematics Subject Classification:  35A01, 35F61, 35Q35, 35B65.

Received: January 2009;      Revised: February 2010;      Available Online: September 2010.