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DIFFUSION-WAVE TYPE SOLUTIONS WITH TWO FRONTS TO A NONLINEAR DEGENERATE REACTION-DIFFUSION SYSTEM

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Abstract

Diffusion-wave type solutions are constructed and investigated for a nonlinear parabolic reaction-diffusion system. The statement of the problem in which mismatched zero fronts are set for different desired functions is considered for the first time. The existence and uniqueness theorem of solutions in the form of series in a class of piecewise analytic functions is proven. It is proposed to construct the desired type of approximate solutions using a step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions. Calculations are performed, and the results of these calculations are verified using the series segments. The behavior of the constructed solutions is numerically analyzed.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, 664033, Irkutsk, Russia

    A. L. Kazakov

  2. Gorkunov Institute of Engineering Science, Ural Branch, Russian Academy of Sciences, 620049, Yekaterinburg, Russia

    L. F. Spevak

Authors
  1. A. L. Kazakov
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  2. L. F. Spevak
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Correspondence to L. F. Spevak.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2022, Vol. 63, No. 6, pp. 104-115. https://doi.org/10.15372/PMTF20220612.

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Kazakov, A.L., Spevak, L.F. DIFFUSION-WAVE TYPE SOLUTIONS WITH TWO FRONTS TO A NONLINEAR DEGENERATE REACTION-DIFFUSION SYSTEM. J Appl Mech Tech Phy 63, 995–1004 (2022). https://doi.org/10.1134/S0021894422060128

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