Temporal growth and eventual periodicity for dispersive wave equationsin a quarter plane

Jerry Bona; Jiahong Wu

doi:10.3934/dcds.2009.23.1141

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2009, Volume 23, Issue 4: 1141-1168. Doi: 10.3934/dcds.2009.23.1141

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

Jerry Bona^1, and
Jiahong Wu^2,

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

Received: January 2007

Revised: April 2008

Published: November 2009

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Abstract

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.

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

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