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

Taige Wang; Bing-Yu Zhang

doi:10.3934/dcdsb.2020160

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2021, Volume 26, Issue 2: 1205-1221. Doi: 10.3934/dcdsb.2020160

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

Taige Wang^1, , and
Bing-Yu Zhang^1,

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

^* Corresponding author: Taige Wang
^* Corresponding author: Taige Wang

Received: December 2019

Early access: May 2020

Published: February 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K55, 34K13.

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