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

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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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 (2021). https://doi.org/10.1007/s10884-020-09938-0

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Keywords

  • Schrödinger equation
  • Half-wave equation
  • Global attractor
  • Fractal dimension

Mathematics Subject Classification

  • 35B40
  • 35Q55
  • 76B03
  • 37L30