This article is cited in 2 papers

The Burgers equation with periodic boundary conditions on an interval

A. V. Samokhin

Moscow State Technical University of Civil Aviation, Moscow, Russia

Abstract: We study the asymptotic profile of the solutions of the Burgers equation on a finite interval with a periodic perturbation on the boundary. The equation describes a dissipative medium, and the initial constant profile therefore passes into a wave with a decreasing amplitude. In the low-viscosity case, the asymptotic profile looks like a sawtooth wave (with periodic breaks of the derivative), similar to the known Fay solution on the half-line, but it has some new properties.

Keywords: sawtooth wave, invariant solution, initial–boundary value problem, asymptotic behavior.

PACS: 43.25.+y

MSC: 35Q35, 35Q53

DOI: 10.4213/tmf9075

 English version: Theoretical and Mathematical Physics, 2016, 188:3, 1371–1376

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