ON THE MOTION, AMPLIFICATION, AND BLOW-UP OF FRONTS IN BURGERS-TYPE EQUATIONSWITH QUADRATIC AND MODULAR NONLINEARITY
A singularly perturbed initial-boundary value problem for parabolic equation, called in applications an equation of Burgers type. The conditions of existence are obtained and the asymptotic approximation of a new class of solutions with a moving front is constructed. The results are applied to problems with quadratic and modular nonlinearity and nonlinear amplification. The influence of nonlinear amplification on the propagation and destruction of fronts is revealed. Estimates of localization and time of blow-up are obtained.