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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Lakeyev A. V.
,
Daneev A. V.
,
Rusanov V. A.
ON BILINEAR DIFFERENTIAL REALIZATION OF A CONTINUAL BEAM OF TRAJECTORY CURVES IN THE CONSTRUCTIONS OF THE RAYLEIGH– RITZ OPERATOR // BSU bulletin. Mathematics, Informatics. - 2020. №1. . - С. 11-27.
Title:
ON BILINEAR DIFFERENTIAL REALIZATION OF A CONTINUAL BEAM OF TRAJECTORY CURVES IN THE CONSTRUCTIONS OF THE RAYLEIGH– RITZ OPERATOR
Financing:
Codes:
DOI: 10.18101/2304-5728-2020-1-11-27UDK: 517. 93, 517.937
Annotation:
We present functional and geometric conditions (necessary and sufficient) for the ex- istence of five non-stationary bilinear operators in a model of differential realization of a continuous bundle of controlled trajectory curves (dynamic processes of the power input / output type) in the class of the second order bilinear non-autonomous ordinary differential equations (including quasi-linear hyperbolic models) in a real parallel Hilbert space. The problem under consideration is a type of non-stationary nonlinear coefficient inverse problems for evolutionary equations in Hilbert space and is solved on the basis of a qualitative study of the continuity property of the Ray- leigh-Ritz functional operator. It is shown that the structure of the fundamental group of the image of this operator depends on the dimension of the projective space on which it acts. The results obtained are applied to the qualitative theory of non-linear structural identification of higher order multilinear non-stationary differential models.
Keywords:
nonlinear inverse problems; bilinear non-stationary differential realization; the Rayleigh-Ritz operator; the Poincaré group.
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