Abstract:
For a non-linear parabolic reaction-diffusion system, solutions of the diffusion wave type are constructed and investigated. For the first time, the formulation of the problem is considered, which involves the assignment of non-coinciding zero fronts for various desired functions. A theorem on the existence and uniqueness of solutions in the form of series in the class of piecewise analytic functions is proved. To construct approximate solutions of the desired type, a step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions is proposed. Calculations were performed, for the verification of the results of which segments of the series were used. A numerical analysis of the behavior of the constructed solutions was carried out.
Keywords:
reaction–diffusion system, diffusion wave, existence and uniqueness theorem, power series, radial basis functions.
Citation:
A. L. Kazakov, L. F. Spevak, “Solutions to a nonlinear degenerating reaction–diffusion system of the type of diffusion waves with two fronts”, Prikl. Mekh. Tekh. Fiz., 63:6 (2022), 104–115; J. Appl. Mech. Tech. Phys., 63:6 (2022), 995–1004
\Bibitem{KazSpe22}
\by A.~L.~Kazakov, L.~F.~Spevak
\paper Solutions to a nonlinear degenerating reaction–diffusion system of the type of diffusion waves with two fronts
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2022
\vol 63
\issue 6
\pages 104--115
\mathnet{http://mi.mathnet.ru/pmtf234}
\crossref{https://doi.org/10.15372/PMTF20220612}
\elib{https://elibrary.ru/item.asp?id=49930294}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2022
\vol 63
\issue 6
\pages 995--1004
\crossref{https://doi.org/10.1134/S0021894422060128}
Linking options:
https://www.mathnet.ru/eng/pmtf234
https://www.mathnet.ru/eng/pmtf/v63/i6/p104
This publication is cited in the following 2 articles:
A. L. Kazakov, L. F. Spevak, “Diffusion wave initiation problem for a nonlinear parabolic system in the case of spherical and cylindrical symmetry”, J. Appl. Mech. Tech. Phys., 65:4 (2024), 677–687
A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “The Problem of Diffusion Wave Initiation for a Nonlinear Second-Order Parabolic System”, Proc. Steklov Inst. Math. (Suppl.), 321:1 (2023), S109–S126
Citation in format AMSBIB
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