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November/December 2013 Well-posedness and stabilization of a model system for long waves posed on a quarter plane
A.F. Pazoto, G.R. Souza
Adv. Differential Equations 18(11/12): 1165-1188 (November/December 2013).

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.

Citation

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A.F. Pazoto. G.R. Souza. "Well-posedness and stabilization of a model system for long waves posed on a quarter plane." Adv. Differential Equations 18 (11/12) 1165 - 1188, November/December 2013.

Information

Published: November/December 2013
First available in Project Euclid: 4 September 2013

zbMATH: 1273.93131
MathSciNet: MR3129021

Subjects:
Primary: 35Q53 , 93C20 , 93D15

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 11/12 • November/December 2013
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