FAST-SLOW DYNAMICS FOR PARABOLIC PERTURBA TIONS OF CONSERVATION-LAWS

We study the ''large time'' behaviour of parabolic perturbation of hyp erbolic systems endowed with both linearly degenerate and genuinely no n linear fields, with periodic initial data. For ''moderate time'', th e perturbation may often be ignored. For ''large time'', we give a qua litative description of the dynamics, by means of an asymptotic expans ion: at the leading level, the nonlinear modes are damped, whereas the linear mode do propagate according to the perturbation. We describe i n more details the Keyfitz-Kranzer system.