A mathematical model of the wave process with a network carrier

Title	A mathematical model of the wave process with a network carrier
Authors	I. V. Perova¹ ¹Voronezh State University
Annotation	The paper presents an approach to constructing a mathematical model of the wave process of an elastic network structure and sufficient conditions for weak solvability of the corresponding initial boundary value problem. The proof of the theorem of the existence of a weak solution uses the Faedo-Galerkin method with a special basis determined by a system of generalized eigenfunctions of the elliptic operator of the problem [1]. The results obtained can be used in solving problems of optimal control of differential systems in various directions of an applied nature.
Keywords	wave equation, initial boundary value problem, weak solution.
Citation	Perova I. V. ''A mathematical model of the wave process with a network carrier'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 153-157. Available at: https://conf.svmo.ru/files/2024/papers/paper27.pdf. - Date of access: 16.10.2024.