Stabilization of the linear Kawahara equation

Abstract

We study the stabilization of global solutions of the linear Kawahara equation (K) with periodic boundary conditions over the interval (0, 2π) under the effect of a localized dam- ping mechanism. The Kawahara equation is a model for small amplitude long waves. Using separation of variables, the Ingham inequality, multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K) model.