Title | Investigation of the stability for substances' concentrations' dynamics in the catalyst grain's diffusion model |
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Authors | O. S. Yazovtseva^{1}, I. M. Gubaydullin^{2}, A. S. Inshakova^{3}, D. A. Rodkina^{3}^{1}Steklov Mathematical Institute of Russian Academy of Sciences ^{2}Institute of Petrochemistry and Catalysis of RAS ^{3}National Research Mordovia State University |

Annotation | The article proposes a method for studying the solutions' dynamic stability of parabolic system describing a mathematical model of a homogeneous reaction in a catalyst grain. The nonlinear model is constructed using a diffusion approach -- the diffusion of components along the granule's radius, their consumption and formation due to chemical reactions are taken into account. The study of dynamic stability involves the decomposition of solutions into a series by the Galerkin method using continuous basis functions. A nonlinear system of ordinary differential equations with respect to the weight functions is constructed from the orthogonality condition of the residual. Its equilibrium positions are found. The system of ordinary differential equations is linearized at the neighbourhood of each equilibrium. A conclusion is made about the solutions' stability based on the signs of the eigenvalues of the linear approximation. Further, the conclusion is extended to the solutions of the initial system -- the concentration of substances in the catalyst grain model. |

Keywords | parabolic equations, Galerkin method, linearization, dynamic stability, catalyst grain |

Citation | Yazovtseva O. S., Gubaydullin I. M., Inshakova A. S., Rodkina D. A. ''Investigation of the stability for substances' concentrations' dynamics in the catalyst grain's diffusion model'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 277-282. Available at: https://conf.svmo.ru/files/2023/papers/paper45.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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