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IssuesArchive of Issues2018-4pp.397-410

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Total articles in the database: 4893
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V.V. Vasiliev, "Singular Solutions in the Problems of Mechanics and Mathematical Physics," Mech. Solids. 53 (4), 397-410 (2018)
Year 2018 Volume 53 Number 4 Pages 397-410
DOI 10.3103/S0025654418040052
Title Singular Solutions in the Problems of Mechanics and Mathematical Physics
Author(s) V.V. Vasiliev (Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, vvvas@dol.ru)
Abstract A problem of the solutions singularity for applied problems is discussed. It is proposed to qualify such solutions as formal mathematical results that arise from the discrepancy between the mathematical and physical models of the phenomenon or object being studied. As examples, we consider the singular solution of the Schwarzschild problem in the general theory of relativity (serving as the mathematical basis for the existence of objects called the Black Holes), the solution of the mathematical physics problem for a circular membrane loaded in the center by a concentrated force, and the solution for the problems of the theory of elasticity about a cylindrical punch and an expandable plate with a crack. A generalization of the classical definition for a function and its derivative is proposed. This generalization makes it possible to obtain regular solutions of traditional singular problems.
Keywords general theory of relativity, mathematical physics, theory of elasticity, singular solutions
References
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19.  V.V. Vasiliev and S.A. Lurie, "Continuous Model with Microstructure," Komp. Nanost. 7 (1), 25-33 (2015).
20.  V.V. Vasiliev and S.A. Lurie, "Generalized Theory of Elasticity," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 4, 16-27 (2015) [Mech. Solids (Engl. Transl.) 50 (4), 379-388 (2015)]
21.  V.V. Vasiliev and S.A. Lurie, "New Solution of Axisymmetric Contact Problem of Elasticity," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 5, 12-21 (2017) [Mech. Solids (Engl. Transl.) 52 (5), 479-487 (2017)]
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23.  V.V. Vasiliev and S.A. Lurie, "Generalized Solution of the Problem on a Circular Membrane Loaded by a Concentrated Force," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 3, 115-119 (2016) [Mech. Solids (Engl. Transl.) 51 (3), 334-338 (2016)].
24.  V.V. Vasiliev and S.A. Lurie "New Solution of the Plane Problem for an Equilibrium Crack," Izv. Akad. Nauk. Mekh. Tverd. Tela No. 5, 61-67 (2016) [Mech. Solids (Engl. Transl.) 51 (5), 557-561 (2016)].
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Received 05 March 2018
Link to Fulltext https://link.springer.com/article/10.3103/S0025654418040052
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