Solving cauchy problem for elasticity equations in a plane dynamic case

Sergei I. Senashov^a, Irina L. Savostyanova^a, Olga N. Cherepanova<sup>b

a</sup> Reshetnev Siberian State University of Science and Technology, Krasnoyarsk, Russian Federation
^b Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: Equations of elasticity in a plane dynamic case are considered in this paper. The system of equations is replaced by system of first-order differential equations with the same solution. The solution-equivalent system is group fibration of the original system of equations. It is a combination of the resolving and automorphic systems. Special classes of conservation laws are found for the resolving system of equations. These laws allow one to find the solution of the original equations in the form of surface integrals over the boundary of an elastic body.

Keywords: equations of elasticity in a plane dynamic case, Cauchy problem, conservation laws, exact solutions.

UDC: 539.3

Received: 05.09.2024
Received in revised form: 24.10.2024
Accepted: 04.11.2024

Language: English