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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 1, Pages 76–85
DOI: https://doi.org/10.26907/0021-3446-2019-1-76-85 (Mi ivm9433) 		 
On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body

S. N. Timergalieva, R. S. Yakushevb

a Kazan State Achitecture and Civil Engineering University, 1 Zelyonaya str., Kazan, 420043 Russia
b Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2019-1-76-85
Abstract: We study the solvability of a nonlinear boundary-value problem for systems of nonlinear partial differential equations of second order. The aim of the work is the proof the theorem existence for solutions. The 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 principle of compressed mappings.
Keywords: elastic inhomogeneous anisotropic body, equilibrium equations, boundary-value problem, three-dimensional singular integral equations, symbol singular operator, existence theorem.
Received: 02.11.2017
Revised: 02.11.2017
Accepted: 22.03.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 1, Pages 67–75
DOI: https://doi.org/10.3103/S1066369X19010080
Bibliographic databases:
Document Type: Article
UDC: 517.958:539.3
Language: Russian
Citation: S. N. Timergaliev, R. S. Yakushev, “On existence of solutions to spatial nonlinear boundary-value problems for arbitrary elastic inhomogneous anisotropoic body”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 1, 76–85; Russian Math. (Iz. VUZ), 63:1 (2019), 67–75
Citation in format AMSBIB
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\pages 76--85
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\issue 1
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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