ON FRONT MOTION IN THE REACTION–DIFFUSION–ADVECTION PROBLEM WITH KPZ-NONLINEARITY

We obtain an asymptotic approximation to a moving inner layer (front) solution of an initial– boundary value problem for a singularly perturbed parabolic reaction–diffusion–advection equation with KPZnonlinearity. An asymptotic approximation for the velocity of the front is found. To prove the existence and uniqueness of a solution the asymptotic method of differential inequalities is used.