Random uniform exponential attractors for Schrödinger lattice systems with quasi-periodic forces and multiplicative white noise

Sijia Zhang; Shengfan Zhou

doi:10.3934/dcdss.2022056

Article Contents

2023, Volume 16, Issue 3&4: 753-772. Doi: 10.3934/dcdss.2022056

This issue Previous Article Existence and local uniqueness of classical Poisson-Nernst-Planck systems with multi-component permanent charges and multiple cations Next Article Qualitative structure of a discrete predator-prey model with nonmonotonic functional response

Random uniform exponential attractors for Schrödinger lattice systems with quasi-periodic forces and multiplicative white noise

Sijia Zhang and
Shengfan Zhou^,

College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China

^* Corresponding author: Shengfan Zhou
^* Corresponding author: Shengfan Zhou

Celebrating the 80th Birthday of Professor Jibin Li

Received: December 2021

Revised: January 2022

Early access: March 2022

Published: March 2023

The second author is supported by NSF of China grant 11871437

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Abstract

We mainly consider the existence of random uniform exponential attractors for Schrödinger lattice systems with quasi-periodic forces and multiplicative white noise. We first give an existence criterion for a random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system (NRDS) defined on the space of infinite sequences with complex-valued components. Then we transfer the considered stochastic Schrödinger lattice system into a random system with random parameters and quasi-periodic forces without white noise through Ornstein-Uhlenbeck process, whose solutions generate a jointly continuous NRDS. Thirdly, we prove the existence of a uniform absorbing random set for this NRDS. Fourthly, we construct a bounded closed random set and verify the Lipschitz continuity of the NRDS on this random set, and next we decompose the difference between two solutions into a sum of two parts including some random variables with bounded expectation. Finally, we obtain the existence of a random uniform exponential attractor for the considered system.

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Mathematics Subject Classification: Primary: 37L60, 34F05.

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