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Stabilization of the Kawahara equation with localized damping

2009; EDP Sciences; Volume: 17; Issue: 1 Linguagem: Inglês

10.1051/cocv/2009041

1292-8119

Carlos Frederico Vasconcellos, Patrícia Nunes da Silva,

Navier-Stokes equation solutions

We study the stabilization of global solutions of the Kawahara (K) equation in a bounded interval, under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model. The proof requires of a unique continuation theorem and the smoothing effect of the (K) equation on the real line, which are proved in this work.