Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane

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October 2009, 23(4): 1141-1168. doi: 10.3934/dcds.2009.23.1141

Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane

1.	Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago , 851 S. Morgan Street MC 249, Chicago, Illinois 60607-7045
2.	Department of Mathematics, Oklahoma State University, United States

Received January 2007 Revised April 2008 Published November 2008

Abstract
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Studied here is the large-time behavior and eventual periodicity of solutions of initial-boundary-value problems for the BBM equation and the KdV equation, with and without a Burgers-type dissipation appended. It is shown that the total energy of a solution of these problems grows at an algebraic rate which is in fact sharp for solutions of the associated linear equations. We also establish that solutions of the linear problems are eventually periodic if the boundary data are periodic.

Keywords: Large-time behavior, BBM-Burgers equation, KdV equation, BBM equation, KdV-Burgers equation, eventual periodicity.

Mathematics Subject Classification: Primary: 35Q20, 35B40.

Citation: Jerry Bona, Jiahong Wu. Temporal growth and eventual periodicity for dispersive wave equations in a quarter plane. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1141-1168. doi: 10.3934/dcds.2009.23.1141

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