Exponential attractors for two-dimensional nonlocal diffusion lattice systems with delay

Lin Yang; Yejuan Wang; Peter E. Kloeden

doi:10.3934/cpaa.2022048

Article Contents

2022, Volume 21, Issue 5: 1811-1831. Doi: 10.3934/cpaa.2022048

This issue Previous Article The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines Next Article The number of limit cycles by perturbing a piecewise linear system with three zones

Exponential attractors for two-dimensional nonlocal diffusion lattice systems with delay

1.
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China
2.
Mathematisches Institut, Universität Tübingen, Tübingen 72076, Germany

^* Corresponding author
^* Corresponding author

Received: February 28, 2021

Revised: November 30, 2021

Early access: March 2022

Published: May 2022

This work was supported by the National Natural Science Foundation of China under Grant No. 41875084

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Abstract

In this paper, we study the long term dynamical behavior of a two-dimensional nonlocal diffusion lattice system with delay. First some sufficient conditions for the construction of an exponential attractor are presented for infinite dimensional autonomous dynamical systems with delay. Then, the existence of exponential attractors for the two-dimensional nonlocal diffusion delay lattice system is established by using the new method of tail-estimates of solutions and overcoming the difficulties caused by the nonlocal diffusion operator and the multi-dimensionality.

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Mathematics Subject Classification: Primary: 34K31, 37L05, 37L30, 37L60.

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