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Finite Dimensional Global Attractor for a Fractional Schrödinger Type Equation with Mixed Anisotropic Dispersion

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Abstract

We study the Cauchy problem for a class of nonlinear damped fractional Schrödinger type equation in a two dimensional unbounded domain. Then, we focus on long-time behaviour of the solutions proving that this behaviour is described by the existence of regular finite-dimensional global attractor in the energy space.

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Acknowledgements

The author would like to express his deep gratitude to the referee for his careful reading as well as for his helpful comments and suggestions leading to the improvement of this work.

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  1. Brahim Alouini

    Present address: I.P.E.I. Monastir, Ibn El Jazzar Street, 5019, Monastir, Tunisia

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  1. Research Lab 18ES17: Analysis, Probability and Fractals, University of Monastir, Faculty of Sciences of Monastir, Monastir, Tunisia

    Brahim Alouini

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  1. Brahim Alouini
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Correspondence to Brahim Alouini.

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In memory of Pr. Ezzeddine Zahrouni.

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Alouini, B. Finite Dimensional Global Attractor for a Fractional Schrödinger Type Equation with Mixed Anisotropic Dispersion. J Dyn Diff Equat 34, 1237–1268 (2022). https://doi.org/10.1007/s10884-020-09938-0

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  • DOI: https://doi.org/10.1007/s10884-020-09938-0

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