Geodesic
Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 4, pp. 64-78

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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
Mots-clés : diffusion wave. 
@article{SJIM_2021_24_4_a4,
     author = {A. L. Kazakov and P. A. Kuznetsov and L. F. Spevak},
     title = {Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {64--78},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_4_a4/}
}
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A. L. Kazakov; P. A. Kuznetsov; L. F. Spevak. Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 4, pp. 64-78. http://geodesic.mathdoc.fr/item/SJIM_2021_24_4_a4/