UDK 539.371
CONSERVATION LAWS EQUATIONS PLANE THEORY OF ELASTICITY
S. I. Senashov, E. V. Filyushina
Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation E-mail: sen@sibsau.ru, filyushina@sibsau.ru
Today for a full study of differential equations in addition to defining the type of equations and the correct formulation of the boundary conditions, determine the existence and uniqueness of solutions it is necessary to know the symmetry allowed by the system and conservation laws. It turns out that in addition to well-known laws of conservation of the following general methods for constructing equations, there are other conservation laws. These laws can be useful for solving boundary value problems and get different estimates of the solutions. In the paper, we construct new conservation laws for the two-dimensional equations of linear elasticity in the stationary case. Conserved current is linear in the first derivatives of the unknown functions, but does not depend on the unknown functions themselves. Constructed conservation laws can be used for solving boundary value problems of elasticity theory for finite fields.
laws of conservation, elasticity theory, the conserved current.
References
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- Senashov S. I., Gomonova O. V., Jahno A. N. Matematicheskie voprosy dvumernyh uravnenij ideal'noj plastichnosti (Mathematical questions of two-dimensional equations of ideal plasticity). Krasnoyarsk, SibGAU, 2012, p. 137.
- Senashov S. I. Jahno A. N. Vestnik ChGPU. 2013, no. 2(16), p. 107–115.
- Senashov S. I., Cherepanova O. I., Kondrin A. V. Vestnik SibGAU. 2013, no. 3(49), p. 100–103.
Senashov Sergey Ivanovich – Doctor of Phisical and Mathematical Sciences, professor, head of the Department of Information economic systems, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: sen@sibsau.ru
Filyushina Elena Vladimirovna – assistant of the Department of Information economic systems, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: filyushina@sibsau.ru
