The Linear Kawahara Equation on the Half-Line

Abstract

We study the stabilization of global solutions of the Linear Kawahara (K) equation posed on the right half-line, under the effect of a localized damping mechanism. In this work we analyze the existence, uniqueness and regularity of solutions for the (K) equation, using semigroups theory and since this system is defined on an unbounded domain, a special multiplier argument is showed. To prove the exponential decay of the energy associated to (K) system, due to a lack of compactness, we use local compactness arguments and multipliers techniques. The Kawahara equation describes the evolution of small amplitude long waves in problems arising in fluid dynamics.