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

Pages: 709 - 717, Issue special, November 2013

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Changming Song - College of Science, Zhongyuan University of Technology, No.41, Zhongyuan Middle Road, Zhengzhou 450007, China (email)
Hong Li - College of Science, Zhongyuan University of Technology, No.41, Zhongyuan Middle Road, Zhengzhou 450007, China (email)
Jina Li - College of Science, Zhongyuan University of Technology, No.41, Zhongyuan Middle Road, Zhengzhou 450007, China (email)

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.

Received: September 2012;      Revised: February 2013;      Published: November 2013.

 References