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This article is cited in 4 scientific papers (total in 4 papers)
Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system
A. L. Kazakova, P. A. Kuznetsova, L. F. Spevakbc a Matrosov Institute for System Dynamics and Control Theory SB RAS, ul. Lermontova 134, Irkutsk 664033, Russia
b Ural State University of Railway Transport, ul. Kolmogorova 66, Ekaterinburg 620034, Russia
c Ural State University of Railway Transport,
ul. Kolmogorova 66, Ekaterinburg 620034, Russia
Abstract:
The paper considers 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 the analytical solution having the diffusion-wave type at a given wave
front. The proof is constructive, and the solution is constructed in the form of
a power series with recursively calculated coefficients. Besides, we propose
a numerical algorithm based on the boundary element method. For its verification,
we use segments of analytical solutions.
Keywords:
nonlinear parabolic equations with singularity, reaction-diffusion system,
power series, existence and uniqueness theorem, boundary element method,
computational experiment, diffusion wave.
Received: 11.05.2021 Revised: 11.05.2021 Accepted: 21.10.2021
Citation:
A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system”, Sib. Zh. Ind. Mat., 24:4 (2021), 64–78
Linking options:
https://www.mathnet.ru/eng/sjim1152 https://www.mathnet.ru/eng/sjim/v24/i4/p64
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Abstract page: | 221 | Full-text PDF : | 78 | References: | 26 | First page: | 18 |
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