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This article is cited in 9 scientific papers (total in 9 papers)
MATHEMATICS
On the motion, amplification, and blow-up of fronts in Burgers-type equations with quadratic and modular nonlinearity
N. N. Nefedova, O. V. Rudenkoabc 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.
Received: 26.05.2020 Revised: 08.06.2020 Accepted: 09.06.2020
Citation:
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., 493 (2020), 26–31; Dokl. Math., 102:1 (2020), 283–287
Linking options:
https://www.mathnet.ru/eng/danma90 https://www.mathnet.ru/eng/danma/v493/p26
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