UNIFORM ATTRACTOR FOR NON-AUTONOMOUS NONLINEAR SCHRODINGER EQUATION

作者：Goubet Olivier^*; Kechiche Wided

来源：Communications on Pure and Applied Analysis, 2011, 10(2): 639-651.

DOI：10.3934/cpaa.2011.10.639

• Uniform attractor
• nonlinear Schrodinger equations
• upper semicontinuity
• non-autonomous dynamical systems

We consider a weakly coupled system of nonlinear Schrodinger equations which models a Bose Einstein condensate with an impurity. The first equation is dissipative, while the second one is conservative. We consider this dynamical system into the framework of non-autonomous dynamical systems, the solution to the conservative equation being the symbol of the semi-process. We prove that the first equation possesses a uniform attractor, which attracts the solutions for the weak topology of the underlying energy space. We then study the limit of this attractor when the coupling parameter converges towards 0.

• 出版日期2011-3
• 单位INRIA