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| Open Access | REGULARIZATION OF THE SOLUTION OF THE CAUCHY PROBLEM FOR A SYSTEM OF EQUATIONS OF ELASTICITY THEORY IN AN INFINITE DOMAIN
Usanov Kamoliddin Xolboyevich, To’xtayev Zuxriddin O’ktamovich , Samarkand Institute of Economics and ServiceAbstract
The paper discusses continuation of a solution of the elasticity system in a domain from its values and the values of its stresses on part of the boundary, i.e. the Cauchy problem for the Lame system.
Keywords
Cauchy problem, Lame system, Elasticity theory, Infinite domain, Carleman matrix, Carleman function, Regularization, Fundamental solutions, Laplace operator, Harmonic function.
References
Yarmukhamedov Sh. On the Cauchy problem for the Laplace equation. DAN SSSR, 1977, vol. 235, no. 2, pp. 281-283.
Makhmudov O. I., Niyozov I. E. The Cauchy problem for the system of elasticity equations in an infinite domain // Uzbek Mathematical Journal. 2006. No. 4. pp. 44-53.
Makhmudov O., Niyozov I. The Cauchy problem for the Lame system in infinite domains in // Journal of Inverse and Ill-Posed Problems. V14. N9. 2006. pp. 905-924(20).
Kupradze V. D., Burchuladze T. V., Gegelia T. G., et al. Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Classical and micropolar theory. Statics, harmonic oscillations, dynamics. Fundamentals and methods of solution. Moscow: Nauka, 1976.
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