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Open Access Research

Averaging of the 3D non-autonomous Benjamin-Bona-Mahony equation with singularly oscillating forces

Mingxia Zhao1, Xinguang Yang2* and Lingrui Zhang3

Author affiliations

1 College of Mathematics and Information Science, Pingdingshan University, Pingdingshan, 467009, P.R. China

2 College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, P.R. China

3 College of Education and Teacher Development, Henan Normal University, Xinxiang, 453007, P.R. China

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Citation and License

Boundary Value Problems 2013, 2013:111  doi:10.1186/1687-2770-2013-111

Published: 30 April 2013

Abstract

For <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M1">View MathML</a>, we investigate the convergence of corresponding uniform attractors of the 3D non-autonomous Benjamin-Bona-Mahony equation with singularly oscillating force contrast with the averaged Benjamin-Bona-Mahony equation (corresponding to the limiting case <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M2">View MathML</a>). Under suitable assumptions on the external force, we shall obtain the uniform boundedness and convergence of the related uniform attractors as <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/111/mathml/M3">View MathML</a>.

MSC: 35B40, 35Q99, 80A22.

Keywords:
Benjamin-Bona-Mahony equation; singularly oscillating forces; uniform attractors; translational bounded functions