# American Institute of Mathematical Sciences

February  2021, 26(2): 1205-1221. doi: 10.3934/dcdsb.2020160

## Forced oscillation of viscous Burgers' equation with a time-periodic force

 1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA

* Corresponding author: Taige Wang

Received  December 2019 Published  May 2020

This paper is concerned about the existence of periodic solutions of the viscous Burgers' equation when a forced oscillation is prescribed. We establish the existence theory by contraction mapping in $H^s[0,1]$ with $s\ge 0$. Asymptotical periodicity is obtained as well, and the periodic solution is achieved by selecting a suitable function as initial data to generate a solution and passing time limit to infinity. Moreover, uniqueness and global stability is achieved for this periodic solution.

Citation: Taige Wang, Bing-Yu Zhang. Forced oscillation of viscous Burgers' equation with a time-periodic force. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1205-1221. doi: 10.3934/dcdsb.2020160
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