Differential and Integral Equations
- Differential Integral Equations
- Volume 13, Number 1-3 (2000), 311-340.
Attractor for a damped cubic-Schrödinger equation on a two-dimensional thin domain
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.
Differential Integral Equations, Volume 13, Number 1-3 (2000), 311-340.
First available in Project Euclid: 21 December 2012
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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