On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions

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Patricia N. da Silva, Carlos F. Vasconcellos, On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions, Int. J. Anal. Appl., 7 (2) (2015), 96-103.

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Patricia N. da Silva, Carlos F. Vasconcellos

Abstract

We study the stabilization of global solutions of the linear Kawahara equation (K) with periodic boundary conditions under the effect of a localized damping 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.

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