Published 2006-04-13
Keywords
- Evolution equations,
- gain in regularity,
- sobolev space,
- numerical methods
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Abstract
We are concerned with the initial-boundary-value problem associated to the Korteweg - de Vries - Kawahara (KdVK) equation, which is a transport equation perturbed by dispersive terms of 3rd and 5th order. The (KdVK) equation appears in several fluid dynamics problems. We obtain local smoothing effects that are uniform with respect to the size of the interval. We also propose a simple finite-difference scheme for the problem and prove its stability. Finally, we give some numerical examples.
