The Long Time Behavior of Periodic Entropy Solutions to Degenerate Nonlinear Parabolic Equations

Resumo

We establish the asymptotic convergence of an entropy solution, periodic with respect to the spatial variable, of a degenerate nonlinear parabolic equation to a traveling wave. It is shown that, on a segment containing the essential values of the limit profile, the flow function is linear (with the angular coefficient equal to the traveling wave velocity) and the diffusion function is constant.