Initial boundary value problem for the singularly perturbedBoussinesq-type equation

Changming Song; Hong Li; Jina Li

doi:10.3934/proc.2013.2013.709

Article Contents

2013, Volume 2013: 709-717. Doi: 10.3934/proc.2013.2013.709 open access

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Initial boundary value problem for the singularly perturbed Boussinesq-type equation

1.
College of Science, Zhongyuan University of Technology, No.41, Zhongyuan Middle Road, Zhengzhou 450007

Received: August 31, 2012

Revised: January 31, 2013

Published: October 2013

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Abstract

We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to $1/3$. The existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the singularly perturbed Boussinesq-type equation are proved.

Keywords:

Singularly perturbed Boussinesq-type equation,
initial boundary value problem,
global generalized solution,
global classical solution,
Boussinesq equation.

Mathematics Subject Classification: Primary: 35A01, 35L35; Secondary: 35G31, 35Q35.

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