asymmetric two-dimensional elasticity, conservation laws, boundary value problem.

When solving the problem of group classification of equations describing the motion of a purely mechanical continuum, some new systems of differential equations have appeared that can be used to describe real physical processes. One of such new systems is the asymmetric theory of elasticity. This system can be used for materials with a small Young’s modulus, as well as for materials that operate at loads close to critical. In this paper, the equations of the asymmetric theory of elasticity are studied on the basis of their group bundle: decomposition of the system into automorphic and resolving systems, which are systems of differential equations of the first order. Infinite series of conservation laws are constructed for a resolving system of equations and an automorphic system. These laws made it possible to solve the Dirichlet boundary value problem for the asymmetric theory of elasticity in the two-dimensional case. The solutions are constructed in the form of quadratures, which are calculated along the contour of the studied area.

Senashov Sergei Ivanovich e-mail: sen@sibsau.ru, Dr. Sci. Phys. & Math., Professor, Reshetnev Siberian State University of Science and Technology , Krasnoyarsk, Russia.

Savostyanova Irina Leonidovna e-mail: savostyanova@sibsau.ru, Ph.D. in Pedagogy, Reshetnev Siberian State University of Science and Technology , Krasnoyarsk, Russia.