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

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 4 September 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

Export citation