Electron. J. Diff. Eqns., Vol. 2007(2007), No. 06, pp. 1-18.

Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

Eleni Bisognin, Vanilde Bisognin, Octavio Paulo Vera Villagran

Abstract:
We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

Submitted August 2, 2006. Published January 2, 2007.
Math Subject Classifications: 35K60, 93C20.
Key Words: Higher order nonlinear Schrodinger equation; stabilization; localized damping.

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Eleni Bisognin
Centro Universitário Franciscano-UNIFRA
Rua dos Andrade 1614, CEP: 97010-032
Santa Maria, R. S., Brasil
email: eleni@unifra.br
Vanilde Bisognin
Centro Universitário Franciscano-UNIFRA
Rua dos Andrade 1614, CEP: 97010-032
Santa Maria, R. S., Brasil
email: vanilde@unifra.br
Octavio Paulo Vera Villagrán
Departamento de Matemática
Universidad del Bío-Bío
Collao 1202, Casilla 5-C, Concepción, Chile
email: overa@ubiobio.cl   octavipaulov@yahoo.com

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