Abstract

A singularly perturbed initial-boundary value problem for a parabolic equation, which is called in applications an equation of Burgers type, is considered. Existence conditions are obtained, and an 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 for the blow-up localization and blow-up time are obtained.

中文翻译：

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具有二次和模非线性的Burgers型方程的前沿的运动，放大和爆裂

摘要

考虑了抛物方程的奇摄动初值问题，在应用中称其为Burgers型方程。得到了存在条件，并构造了具有移动前沿的一类新解的渐近逼近。该结果适用于具有二次和模非线性和非线性放大的问题。揭示了非线性放大对前沿传播和破坏的影响。获得爆破定位和爆破时间的估计。