The asymptotic behaviour of solutions of the forced Burgers equation on the circle
Résumé
We describe the asymptotic behaviour of entropy solutions of the inviscid Burgers equation on the circle with time-periodic forcing. These solutions converge to periodic states, but the period of these limit states may be greater than the period of the forcing. A corollary is that the only solutions without shocks are periodic. This result can be interpreted in terms of the invariant curves of the associated dynamics.
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