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Front Motion in a Problem with Weak Advection in the Case of a Continuous Source and a Modular-Type Source

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Abstract

We obtain an asymptotic approximation to a moving inner layer (front) solution of an initial–boundary value problem for a singularly perturbed parabolic reaction–advection–diffusion equation with small advection. We separately consider the case of a continuous source (the nonlinearity describing the interaction and reaction) and the case of a source discontinuity for a certain value of the unknown function, which arises in a number of topical applications. For either problem, an asymptotic approximation to the solution is constructed and existence and uniqueness theorems for such a solution are proved.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 18-11-00042.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. N. Nefedov, E. I. Nikulin & A. O. Orlov

Authors
  1. N. N. Nefedov
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  2. E. I. Nikulin
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  3. A. O. Orlov
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Corresponding authors

Correspondence to N. N. Nefedov, E. I. Nikulin or A. O. Orlov.

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Translated by V. Potapchouck

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Nefedov, N.N., Nikulin, E.I. & Orlov, A.O. Front Motion in a Problem with Weak Advection in the Case of a Continuous Source and a Modular-Type Source. Diff Equat 58, 757–770 (2022). https://doi.org/10.1134/S0012266122060052

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  • DOI: https://doi.org/10.1134/S0012266122060052

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