Solutions to the burgers equation with periodic perturbations on boundary - A. V. Samokhin (Научный вестник МГТУ ГА, 2016)
The asymptotic behavior of solutions of the Burgers equation with initial value - boundary problem on a finite interval with periodic boundary conditions is studied. The equation describes a dissipative medium, so a constant initial profile will evolve to a travelling-wave solution. Its asymptotic limit is periodic ’sawtooth’ solution with periodical breaks of derivative, similar to the Fay solution on a half-line.