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

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 nonli...

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Bibliographic Details
Published in:Russian mathematics 2019-01, Vol.63 (1), p.67-75
Main Authors: Timergaliev, S. N., Yakushev, R. S.
Format: Article
Language:English
Subjects:
Boundary value problems
Elastic anisotropy
Existence theorems
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear differential equations
Nonlinear equations
Operators (mathematics)
Partial differential equations
Singular integral equations
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Summary: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X19010080