Control and stabilization of the Kawahara equation on a periodic domain
نویسندگان
چکیده
منابع مشابه
Control and Stabilization of the Kawahara Equation on a Periodic Domain
In this paper, we study a class of distributed parameter control system described by the Kawahara equation posed on a periodic domain T (a unit circle in the plane) with an internal control acting on an arbitrary small nonempty subdomain of T. Aided by the Bourgain smoothing property of the Kawahara equation on a periodic domain, we show that the system is locally exactly controllable and expon...
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This paper aims at completing an earlier work of Russell and Zhang [38] to study internal control problems for the distributed parameter system described by the Korteweg-de Vries equation on a periodic domain T. In [38], Russell and Zhang showed that the system is locally exactly controllable and locally exponentially stabilizable when the control acts on an arbitrary nonempty subdomain of T. I...
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It was proved by Linares and Ortega in [24] that the linearized Benjamin-Ono equation posed on a periodic domain T with a distributed control supported on an arbitrary subdomain is exactly controllable and exponentially stabilizable. The aim of this paper is to extend those results to the full Benjamin-Ono equation. A feedback law in the form of a localized damping is incorporated in the equati...
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In this paper, we investigate a damped Korteweg-de Vries equation with forcing on a periodic domain $mathbb{T}=mathbb{R}/(2pimathbb{Z})$. We can obtain that if the forcing is periodic with small amplitude, then the solution becomes eventually time-periodic.
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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 sm...
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ژورنال
عنوان ژورنال: Communications in Information and Systems
سال: 2012
ISSN: 1526-7555,2163-4548
DOI: 10.4310/cis.2012.v12.n1.a4