On the asymptotic behavior of solutions to a dissipative nonlocal NLS type equation
Brahim Alouini
University of Monastir, Faculty of Sciences of Monastir, Research Laboratory Analysis, Probabilities and Fractals LR18ES17 Tunisia
Co-Author(s):
Abstract:
This talk addresses the long-time dynamics of a damped nonlinear Schr\{o}dinger type equation on $\mathbb{R}$ involving a nonlocal integral term.
Under the minimal assumption on the external source and for a broad class of smooth subcritical nonlinearities, we prove, using a recent idea, the existence of a compact global attractor and an exponential attractor in the Sobolev space $H^1(\mathbb{R})$. Moreover, combining quasi-stability and localization arguments, we derive explicit upper bounds on the Hausdorff and fractal dimensions of the global attractor in terms of the physical parameters.
