# American Institute of Mathematical Sciences

## Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays

 1 Department of Mathematics, Northwest Normal University, Lanzhou 730070, China 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 3 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

* Corresponding author: Pengyu Chen

Received  September 2020 Revised  February 2021 Published  March 2021

Fund Project: Research supported by National Natural Science Foundations of China (No. 12061063, No. 12061062, No. 11771428), Natural Science Foundation of Gansu Province (No. 20JR5RA522), Science Research Project for Colleges and Universities of Gansu Province (No. 2019B-047), Project of NWNU-LKQN2019-3 and Project of NWNU-LKQN2019-13

In this paper, we investigate the global existence, uniqueness and asymptotic stability of time periodic classical solution for a class of extended Fisher-Kolmogorov equations with delays and general nonlinear term. We establish a general framework to investigate the asymptotic behavior of time periodic solutions for nonlinear extended Fisher-Kolmogorov equations with delays and general nonlinear function, which will provide an effective way to deal with such kinds of problems. The discussion is based on the theory of compact and analytic operator semigroups and maximal regularization method.

Citation: Pengyu Chen, Xuping Zhang, Zhitao Zhang. Asymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov equations with delays. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021103
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