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Article Dans Une Revue Nonlinearity Année : 2005

The asymptotic behaviour of solutions of the forced Burgers equation on the circle

Patrick Bernard
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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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Dates et versions

hal-01251197 , version 1 (06-01-2016)

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Patrick Bernard. The asymptotic behaviour of solutions of the forced Burgers equation on the circle. Nonlinearity, 2005, 18, pp.101-124. ⟨10.1088/0951-7715/18/1/006⟩. ⟨hal-01251197⟩
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