Corner layer properties and intermediate asymptotics of waiting time solutions of nonlinear diffusion equations

CARLOS ALBERTO PERAZZO; CLAUDIO LIONEL MARTIN VIGO; JULIO GRATTON

International Journal of Heat and Technology

Edizioni ETS

Año: 2003 vol. 21 p. 121 - 128

Heat conduction by electrons in plasmas and by radiation in partially and fully ionized gases as well as other phenomena like flows in porous media, viscous-gravity currents, etc. obey nonlinear diffusion equations and are characterized by a finite propagation velocity. Under certain conditions the waiting-time phenomenon occurs, consisting of a lapse in which the front of the thermal wave sits motionless, while its profile changes and a moving corner layer (a small region where the temperature gradient varies rapidly) develops. Previously we solved numerically the nonlinear diffusion equation for power law initial pro-files and investigated the dependence of the waiting time on the initial conditions and the nonlinearity parameter. Here we analyze the evolution and motion of the corner layer. We find that the corner layer velocity on arriving at the front coincides with the front velocity at start-up. We investigate the intermediate asymptotics close to the front and near start-up. We detect two self-similar regimes. The first one is a constant velocity traveling wave that appears in a domain close to the corner layer. The second is a different type of self-similarity and occurs behind the corner layer but a little farther from it than the first re-gime.