Front Motion in a Reaction–Diffusion–Advection Problemwith a 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 a KPZ-nonlinearity. 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.