GLOBAL STABILIZATION OF A COUPLED SYSTEM OF TWO GENERALIZED KORTEWEG-DE VRIES TYPE EQUATIONS POSED ON A FINITE DOMAIN

被引：8

作者：

Nina, Dugan ^{[1
]}

Pazoto, Ademir F. ^{[1
]}

Rosier, Lionel ^{[2
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, RJ, Brazil

[2] CNRS, INRIA, UHP, Inst Elie Carton,UMR 7502, F-54506 Vandoeuvre Les Nancy, France

来源：

MATHEMATICAL CONTROL AND RELATED FIELDS | 2011年 / 1卷 / 03期

关键词：

Exponential Decay; Korteweg-de Vries equation; Stabilization; CONTROLLABILITY;

D O I：

10.3934/mcrf.2011.1.353

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this work is to study the internal stabilization of a coupled system of two generalized Korteweg-de Vries equations under the effect of a localized damping term. The exponential stability, as well as, the global existence of weak solutions are investigated when the exponent in the nonlinear term ranges over the interval [1,4) . To obtain the decay we use multiplier techniques combined with compactness arguments and reduce the problem to prove a unique continuation property for weak solutions. Here, the unique continuation is obtained via the usual Carleman estimate.

引用

页码：353 / 389

页数：37

共 23 条

[1] NONLINEAR-EVOLUTION EQUATIONS OF PHYSICAL SIGNIFICANCE [J].

ABLOWITZ, MJ ;

KAUP, DJ ;

NEWELL, AC ;

SEGUR, H .

PHYSICAL REVIEW LETTERS, 1973, 31 (02) :125-127

[2] Stability and instability of solitary waves for a nonlinear dispersive system [J].

Alarcon, E ;

Angulo, J ;

Montenegro, JF .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 36 (08) :1015-1035

[3]

[Anonymous], 1998, An Introduction to Semilinear Evolution Equations

[4]

Bisognin E., 2003, Adv. Differ. Equ, V8, P443

[5] A MODEL SYSTEM FOR STRONG INTERACTION BETWEEN INTERNAL SOLITARY WAVES [J].

BONA, JL ;

PONCE, G ;

SAUT, JC ;

TOM, MM .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 143 (02) :287-313

[6] A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain [J].

Bona, JL ;

Sun, SM ;

Zhang, BY .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (7-8) :1391-1436

[7]

Davila M., 1994, THESIS FEDERAL U RIO

[8]

GEAR JA, 1984, STUD APPL MATH, V70, P235

[9] On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping [J].

Linares, F. ;

Pazoto, A. F. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (05) :1515-1522

[10]

Linares F, 2004, COMMUN PUR APPL ANAL, V3, P417

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