Advances in Differential Equations

Well-posedness and stabilization of a model system for long waves posed on a quarter plane

A.F. Pazoto and G.R. Souza

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Abstract

In this paper we are concerned with an initial--boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized damping term. The model arises when modeling the propagation of long waves generated by a wave maker in a channel. It is shown that the solutions of the system are exponentially stable and globally well-posed in the weighted space $L^2(e^{2bx}\,dx)$ for $b>0$. The stabilization problem is studied using a Lyapunov approach, while the well-posedness result is obtained combining fixed-point arguments and energy-type estimates.

Article information

Source
Adv. Differential Equations Volume 18, Number 11/12 (2013), 1165-1188.

Dates
First available in Project Euclid: 4 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1378327382

Mathematical Reviews number (MathSciNet)
MR3129021

Zentralblatt MATH identifier
1273.93131

Subjects
Primary: 93D15: Stabilization of systems by feedback 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 93C20: Systems governed by partial differential equations

Citation

Pazoto, A.F.; Souza, G.R. Well-posedness and stabilization of a model system for long waves posed on a quarter plane. Adv. Differential Equations 18 (2013), no. 11/12, 1165--1188. https://projecteuclid.org/euclid.ade/1378327382.


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