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Construction of solutions to a degenerate reaction-diffusion system with a general nonlinearity in the cases of cylindrical and spherical symmetry
A. L. Kazakova, P. A. Kuznetsova, L. F. Spevakb a Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
b Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg
Abstract:
We consider a reaction-diffusion system with a general nonlinearity with cylindrical or spherical symmetry. For this system, we find a solution of the diffusion-wave type propagating over a zero background with a finite velocity. The solution is constructed as a Taylor series with recurrent coefficients whose convergence is proved by the majorant method and the Cauchy–Kovalevskaya theorem. The research is supplemented by numerical calculations based on the expansion in radial basis functions. This paper continues a series of our publications devoted to the study of wave-type solutions in the class of analytical functions.
Keywords:
reaction-diffusion system, diffusion wave, power series, majorant method, radial basis functions, computational experiment.
Citation:
A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak, “Construction of solutions to a degenerate reaction-diffusion system with a general nonlinearity in the cases of cylindrical and spherical symmetry”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 213, VINITI, Moscow, 2022, 54–62
Linking options:
https://www.mathnet.ru/eng/into1048 https://www.mathnet.ru/eng/into/v213/p54
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Abstract page: | 87 | Full-text PDF : | 30 | References: | 18 |
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