N. N. Nefedov, O. V. Rudenko, “On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity”, Dokl. RAN. Math. Inf. Proc. Upr., 2020, Volume 493,Pages <nobr>26

This article is cited in 11 papers

MATHEMATICS

On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity

N. N. Nefedov^a, O. V. Rudenko^abc

^a Lomonosov Moscow State University, Moscow, Russian Federation
^b Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, Russian Federation
^c Institute of Physics of the Earth, Russian Academy of Scienses, Moscow, Russian Federation

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.

Keywords: singularly perturbed parabolic problems, equations of Burgers type, reaction–diffusion–advection equations, internal layers, fronts, asymptotic, methods, blow-up of solutions.

UDC: 534.222

Received: 26.05.2020
Revised: 08.06.2020
Accepted: 09.06.2020

DOI: 10.31857/S2686954320040141