On Damping Rates of dissipative KdV equations

Jean-Paul Chehab (1, 2) , Georges Sadaka (2)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We consider here different models of dissipative Korteweg-de Vries (KdV) equations on the torus. Using a proper wave function , 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.

Mots clés: Damped KdV equations; long time behavior; inverse problems

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Jean-Paul Chehab, Georges Sadaka. On Damping Rates of dissipative KdV equations. 2012. ⟨hal-00734292⟩