On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification

A singularly perturbed initial–boundary value problem for a parabolic equation known in applications as a Burgers-type or reaction–diffusion–advection equation is considered. An asymptotic approximation of solutions with a moving front is constructed in the case of modular and quadratic nonlinearity and nonlinear amplification. The influence exerted by nonlinear amplification on front propagation and blowing- up is determined. The front localization and the blowing-up time are estimated.