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Russian Mathematics

, Volume 63, Issue 1, pp 67–75 | Cite as

On the Existence of Solutions to Spatial Nonlinear Boundary Value Problems for Arbitrary Elastic Inhomogeneous Anisotropic Body

  • S. N. TimergalievEmail author
  • R. S. YakushevEmail author
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Abstract

We study the solvability of a nonlinear boundary value problem for a system of nonlinear partial differential equations of the second order. The goal of this paper is to prove the existence theorem for solutions to the mentioned problem. This problem is reduced to a system of three-dimensional nonlinear singular integral equations, whose solvability can be proved with the use of the symbol of a singular operator and the contraction mapping principle.

Key words

elastic inhomogeneous anisotropic body equilibrium equations boundary value problem three-dimensional singular integral equations symbol of a singular operator existence theorem 

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Kazan State Achitecture and Civil Engineering UniversityKazanRussia
  2. 2.Kazan Federal UniversityKazanRussia

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