Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system

A. L. Kazakov ; P. A. Kuznetsov ; L. F. Spevak

Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 4, pp. 64-78.

Résumé

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.

Détail

Keywords: nonlinear parabolic equations with singularity, reaction-diffusion system, power series, existence and uniqueness theorem, boundary element method, computational experiment
Mots-clés : diffusion wave.

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