Differential and Integral Equations

Attractor for a damped cubic-Schrödinger equation on a two-dimensional thin domain

Mostafa Abounouh and Olivier Goubet

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Abstract

In this article we prove the existence of an attractor for a dissipative nonlinear Schrödinger equation in the critical case for a two-dimensional thin domain. Moreover we prove that this attractor is smooth, i.e., made of smooth functions when the forcing term is smooth enough. The proofs use a splitting of the Fourier series of the solutions according to the geometry of the domain, together with anisotropic Sobolev inequalities.

Article information

Source
Differential Integral Equations Volume 13, Number 1-3 (2000), 311-340.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356124302

Mathematical Reviews number (MathSciNet)
MR1811961

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B41: Attractors 37L30: Attractors and their dimensions, Lyapunov exponents

Citation

Abounouh, Mostafa; Goubet, Olivier. Attractor for a damped cubic-Schrödinger equation on a two-dimensional thin domain. Differential Integral Equations 13 (2000), no. 1-3, 311--340. https://projecteuclid.org/euclid.die/1356124302.


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