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

  • * Corresponding author: Taige Wang

    * Corresponding author: Taige Wang 
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  • 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.

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


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