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On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification

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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.

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Authors and Affiliations

  1. Faculty of Physics, Moscow State University, Moscow, 119991, Russia

    N. N. Nefedov & O. V. Rudenko

  2. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    O. V. Rudenko

  3. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, 123810, Russia

    O. V. Rudenko

  4. Blekinge Institute of Technology, Karlskrona, Sweden

    O. V. Rudenko

Authors
  1. N. N. Nefedov
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  2. O. V. Rudenko
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Correspondence to O. V. Rudenko.

Additional information

Original Russian Text © N.N. Nefedov, O.V. Rudenko, 2018, published in Doklady Akademii Nauk, 2018, Vol. 478, No. 3, pp. 274–279.

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Nefedov, N.N., Rudenko, O.V. On Front Motion in a Burgers-Type Equation with Quadratic and Modular Nonlinearity and Nonlinear Amplification. Dokl. Math. 97, 99–103 (2018). https://doi.org/10.1134/S1064562418010143

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  • DOI: https://doi.org/10.1134/S1064562418010143

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