Abstract
Recent results for some classes of initial boundary value problem for some classes of Burgers-type equations, for which we investigate moving fronts by using the developed comparison technique, are presented. There are also presented our recent results on singularly perturbed reaction–advection–diffusion problems, which are based on a further development of the asymptotic comparison principle. 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 collapse is determined. The front localization and the collapse time are estimated.
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