Advances in Differential Equations

Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems

D.C. Antonopoulos, V.A. Dougalis, and D.E. Mitsotakis

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study three initial-boundary-value problems for these systems, corresponding, respectively, to nonhomogeneous Dirichlet, reflection, and periodic boundary conditions posed at the endpoints of a finite spatial interval, and establish existence and uniqueness of their solutions. We prove that the initial-boundary-value problem with Dirichlet boundary conditions is well posed in appropriate spaces locally in time, while the analogous problems with reflection and periodic boundary conditions are globally well posed under mild restrictions on the initial data.

Article information

Source
Adv. Differential Equations Volume 14, Number 1/2 (2009), 27-53.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867277

Zentralblatt MATH identifier
1171.35457

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35G25: Initial value problems for nonlinear higher-order equations 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]

Citation

Antonopoulos, D.C.; Dougalis, V.A.; Mitsotakis, D.E. Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems. Adv. Differential Equations 14 (2009), no. 1/2, 27--53. https://projecteuclid.org/euclid.ade/1355867277.


Export citation

Corrections

  • Correction: D.C. Antonopoulos, V.A. Dougalis, D.E. Mitsotakis. Corrigendum to the paper: "Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems". Adv. Differential Equations 14 (2009), no. 9-10, 1019.