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Construction of Solutions to a Boundary Value Problem with Singularity for a Nonlinear Parabolic System

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Abstract

We consider a system of two nonlinear second-order parabolic equations with singularity. Systems of this type are applied in chemical kinetics to describe reaction-diffusion processes. We prove the existence and uniqueness theorem of an analytic solution having the diffusion-wave type at a given wave front. The proof is constructive, and the solution had the form of a power series with recursively calculated coefficients. Moreover, we propose some numerical algorithm based on the boundary element method whose verification uses the segments of analytic solutions.

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Funding

The authors were supported by the Russian Foundation for Basic Research and the Government of the Irkutsk Region (project no. 20–41–385002), and by the Russian Foundation for Basic Research and the Taiwan Ministry of Science and Technology (MOST) (project no. 20–51–S52003).

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Authors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, 664033, Russia

    A. L. Kazakov & P. A. Kuznetsov

  2. Institute of Engineering Science, Ekaterinburg, 620049, Russia

    L. F. Spevak

  3. Ural State University of Railway Transport, Ekaterinburg, 620034, Russia

    L. F. Spevak

Authors
  1. A. L. Kazakov
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  2. P. A. Kuznetsov
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  3. L. F. Spevak
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Correspondence to A. L. Kazakov, P. A. Kuznetsov or L. F. Spevak.

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Kazakov, A.L., Kuznetsov, P.A. & Spevak, L.F. Construction of Solutions to a Boundary Value Problem with Singularity for a Nonlinear Parabolic System. J. Appl. Ind. Math. 15, 616–626 (2021). https://doi.org/10.1134/S1990478921040050

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  • DOI: https://doi.org/10.1134/S1990478921040050

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