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

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


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