Non linear travelling waves with diffusion
arXiv:1203.0727
Abstract
A third order parabolic operator L_εtypical of a non linear wave operator cal L_0 perturbed by viscous terms, is analyzed. Some particular solutions related to L_0 are explicitly determined and the initial value problem for L_εis considered. The parabolic-hyperbolic behaviour is analyzed and rigorous approximations of the solution are achieved.