Geodesic
A generalized solution of an initial boundary value problem arising in the mechanics of discrete-continuous systems
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 1, pp. 84-96.

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In this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a generalized solution, its uniqueness, the correctness of the problem. An analytical formula for the solution is found. Such a system of differential equations arises in the study of discrete-continuum mechanical systems.
Keywords: generalized solution; well-posedness of the problem; discrete-continuum mechanical systems; Timoshenko beam; analytical solution formula. 
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E. P. Kubishkin; O. A. Khrebtyugova. A generalized solution of an initial boundary value problem arising in the mechanics of discrete-continuous systems. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 1, pp. 84-96. http://geodesic.mathdoc.fr/item/MAIS_2012_19_1_a6/

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[2] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1972, 496 pp. | MR