This article is cited in 4 papers

A generalized solution of an initial boundary value problem arising in the mechanics of discrete-continuous systems

E. P. Kubishkin, O. A. Khrebtyugova

P. G. Demidov Yaroslavl State University

Abstract: 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.

UDC: 517.9

Received: 22.11.2011