<b>On the stabilization of the Korteweg–de Vries equation</b> - doi: 10.5269/bspm.v28i2.11215

Vilmos Komornik

doi:10.5269/bspm.v28i2.11215

<b>On the stabilization of the Korteweg–de Vries equation</b> - doi: 10.5269/bspm.v28i2.11215

Vilmos Komornik Université Louis Pasteur

DOI: https://doi.org/10.5269/bspm.v28i2.11215

Keywords: KdV equation. conservation laws, stabilization, decay rate.

Abstract

We consider the Korteweg–de Vries equation on a bounded interval
with periodic boundary conditions. We prove that a natural mass conserving global feedback exponentially stabilizes the system in all Sobolev norms and we obtain explicit decay rates. The proofs are based on the family of conservation laws for the Korteweg–de Vries equation.

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Issue

Vol 28 No 2 (2010)

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Articles

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