Topological-algebraic investigation of the problem of existence of realization of finite-dimensional continuous dynamic processes in the class of second-order ordinary differential equations in a separable Hilbert space has been conducted. Simultaneously, analytical-geometric conditions of continuity of the process of constructing projections for the Rayleigh-Ritz nonlinear functional operator together with computation of the fundamental group of its image have been determined. The results may be applied to a posteriori modeling nonstationary hyperbolic systems.

differential realization, identification of hyperbolic model.

Received: February 1, 2024; Accepted: March 28, 2024; Published: April 22, 2024

How to cite this article: A. V. Lakeyev, V. A. Rusanov, A. V. Banshchikov and R. A. Daneev, On finite character geometrical property of the differential realization of nonstationary hyperbolic systems, Advances in Differential Equations and Control Processes 31(2) (2024), 187-205. https://doi.org/10.17654/0974324324010

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