Geodesic
Construction of solutions to a degenerate reaction-diffusion system with a general nonlinearity in the cases of cylindrical and spherical symmetry
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 54-62

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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.
Mots-clés : reaction-diffusion system, diffusion wave
Keywords: power series, majorant method, radial basis functions, computational experiment. 
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     author = {A. L. Kazakov and P. A. Kuznetsov and L. F. Spevak},
     title = {Construction of solutions to a degenerate reaction-diffusion system with a general nonlinearity in the cases of cylindrical and spherical symmetry},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {54--62},
     publisher = {mathdoc},
     volume = {213},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_213_a4/}
}
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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. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 54-62. http://geodesic.mathdoc.fr/item/INTO_2022_213_a4/