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

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 ≥ 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.