On damping rates of dissipative KdV equations

Jean-Paul Chehab; Georges Sadaka

doi:10.3934/dcdss.2013.6.1487

Article Contents

2013, Volume 6, Issue 6: 1487-1506. Doi: 10.3934/dcdss.2013.6.1487

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On damping rates of dissipative KdV equations

Jean-Paul Chehab^1, and
Georges Sadaka^2,

1.
LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, Pôle Scientique, 33, rue Saint Leu, 80039 Amiens
2.
LAMFA, CNRS UMR 7352, Université de Picardie Jules Verne, Pôle Scientifique, 33, rue Saint Leu, 80039 Amiens

Received: August 31, 2012

Revised: August 31, 2012

Published: November 2013

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Abstract

We consider here different models of dissipative Korteweg-de Vries (KdV) equations on the torus. Using a proper wave function $\Gamma$, we compare numerically the long time behavior effects of the damping models and we propose a hierarchy between these models. We also introduce a method based on the solution of an inverse problem to rebuild a posteriori the damping operator using only samples of the solution.

Keywords:

Mathematics Subject Classification: Primary: 35B40, 35Q53, 65M06, 65M32, 65M70; Secondary: 65L12, 15A29.

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