Asymptotics of the Burgers equation solutions on a nite interval with a periodic perturbation on the boundary are studied. The equation describes a dissipative medium, so the initial constant prole passes into a wave with a decreasing amplitude. In the case of a small viscosity the asymptotic prole looks like a saw (with periodic breaks of the derivative), similar to a known Fay solution on the half-line. Yet on an interval some new properties occur. 6 references.