On Front Motion in a Burgers-Type Equation
with Quadratic and Modular Nonlinearity
and Nonlinear Amplification
N. N. Nefedova and Academician of the RAS O. V. Rudenkoa,b,c,d,*
Translated by I. Ruzanova
a Faculty of Physics, Moscow State University, Moscow, 119991 Russia
b Prokhorov General Physics Institute, Russian Academy
of Sciences, Moscow, 119991 Russia
c Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, 123810 Russia
d Blekinge Institute of Technology, Karlskrona, Sweden
Correspondence to: *e-mail: rudenko@acs366.phys.msu.ru
Received 28 September, 2017
Abstract—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.
DOI: 10.1134/S1064562418010143