Abstract. In this article we consider the Burgers equation with some class of perturbations in one space dimension. Using various energy functionals in appropriate weighted Sobolev spaces rewritten in the variables ξ √ τ and log τ , we prove that the large time behavior of solutions is given by the self-similar solutions of the associated Burgers equation.

This paper dressed the drift perturbation effects on the traveling wave speed in a reaction-diffusion system. We prove the existence of a traveling front solution of a KPP-Fisher equation and we show an asymptotic expansion of her speed. Finally, we discuss according all parameters of our system regions of the plane in which the traveling wave speed increases or decreases as a function of a small parameter ε.