Strong convergence of trajectory attractors for reaction–diffusion systems with random rapidly oscillating terms

Kuanysh A. Bekmaganbetov; Gregory A. Chechkin; Vladimir V. Chepyzhov

doi:10.3934/cpaa.2020106

Article Contents

2020, Volume 19, Issue 5: 2419-2443. Doi: 10.3934/cpaa.2020106

This issue Previous Article Next Article Uniform a priori estimates for elliptic problems with impedance boundary conditions

Strong convergence of trajectory attractors for reaction–diffusion systems with random rapidly oscillating terms

1.
M.V. Lomonosov Moscow State University, Kazakhstan Branch, Kazhymukan st. 11, Astana, 010010, Kazakhstan
2.
Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
3.
M.V. Lomonosov Moscow State University, Moscow, 119991, Russia
4.
Institute of Mathematics with Computing Center. Subdivision of the Ufa, Federal Research Center of Russian Academy of Science, Chernyshevskogo st. 112, Ufa, 450008, Russia
5.
Institute for Information Transmission Problems - Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 127051, Russia
6.
National Research University Higher School of Economics, Myasnitskaya Street 20, Moscow 101000, Russia

^*Corresponding author
^*Corresponding author

Received: May 2019

Revised: November 2019

Published: March 2020

The work is partially supported by the Russian Foundation of Basic Researches (GAC project 18-01-00046 and VVC project 17-01-00515) and Russian Science Foundation (project 20-11-20272). Work of KAB is supported in part by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan AP05132071.

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Abstract

We consider reaction–diffusion systems with random terms that oscillate rapidly in space variables. Under the assumption that the random functions are ergodic and statistically homogeneous we prove that the random trajectory attractors of these systems tend to the deterministic trajectory attractors of the averaged reaction-diffusion system whose terms are the average of the corresponding terms of the original system. Special attention is given to the case when the convergence of random trajectory attractors holds in the strong topology.

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Mathematics Subject Classification: 35B40, 35B41, 35B45, 35Q30.

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