This article is cited in 11 scientific papers (total in 11 papers)
MATHEMATICS
Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set
Abstract:
The subject of the study is pseudo-vertices of a boundary set, which are necessary for the analytical and numerical construction of singular branches of the generalized (minimax) solution of the Dirichlet problem for an eikonal type equation. The case of variable smoothness of the boundary set boundary is considered, under which the order of smoothness at the points of consideration is reduced to the lowest possible value - up to one. Necessary conditions for the existence of pseudo-vertices are obtained, expressed in terms of one-sided partial limits of differential relations, depending on the properties of local diffeomorphisms that determine these points. An example is given that illustrates the application of the results obtained while solving the velocity problem.
Citation:
A. A. Uspenskii, P. D. Lebedev, “Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 59–73
\Bibitem{UspLeb18}
\by A.~A.~Uspenskii, P.~D.~Lebedev
\paper Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 59--73
\mathnet{http://mi.mathnet.ru/vuu620}
\crossref{https://doi.org/10.20537/vm180106}
\elib{https://elibrary.ru/item.asp?id=32697216}
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This publication is cited in the following 11 articles:
P. D. Lebedev, A. A. Uspenskii, “Metod Nyutona pri postroenii singulyarnogo mnozhestva minimaksnogo resheniya v odnom klasse kraevykh zadach dlya uravnenii Gamiltona — Yakobi”, Chelyab. fiz.-matem. zhurn., 9:1 (2024), 63–76
A. A. Uspenskii, P. D. Lebedev, “Alfa-mnozhestva i ikh obolochki:analiticheskie vzaimosvyazi v ploskom sluchae”, Vestnik rossiiskikh universitetov. Matematika, 29:146 (2024), 204–217
Pavel D. Lebedev, Alexander A. Uspenskii, “Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface”, Ural Math. J., 8:2 (2022), 115–126
A. A. Uspenskii, P. D. Lebedev, “O strukture singulyarnogo mnozhestva resheniya v odnom klasse prostranstvennykh zadach upravleniya po bystrodeistviyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 31:3 (2021), 471–486
A. A. Uspenskii, P. D. Lebedev, “On Singularity Structure of Minimax Solution to Dirichlet Problem For Eikonal Type Equation With Discontinuous Curvature of Boundary of Boundary Set”, Ufa Math. J., 13:3 (2021), 126–151
P. D. Lebedev, A. A. Uspenskii, “Postroenie rasseivayuschikh krivykh v odnom klasse zadach bystrodeistviya pri skachkakh krivizny granitsy tselevogo mnozhestva”, Izv. IMI UdGU, 55 (2020), 93–112
P. D. Lebedev, A. A. Uspenskii, “Elementy analiticheskogo konstruktora reshenii v klasse zadach upravleniya po bystrodeistviyu s tselevym mnozhestvom s razryvnoi kriviznoi granitsy”, Vestnik rossiiskikh universitetov. Matematika, 25:132 (2020), 370–386
A. A. Uspenskii, P. D. Lebedev, “Properties of Non Stationer Pseudo Vertex With the Break of Smoothness of the Target Set Boarder Curvature in the Dirichlet Problem to Eikonal Type Equation”, Sib. Electron. Math. Rep., 17 (2020), 2028–2044
P. D. Lebedev, A. A. Uspenskii, “Postroenie resheniya zadachi upravleniya po bystrodeistviyu pri narushenii gladkosti krivizny granitsy tselevogo mnozhestva”, Izv. IMI UdGU, 53 (2019), 98–114
Rodin A.S., Shagalova L.G., “Bifurcation Points of the Generalized Solution of the Hamilton-Jacobi-Bellman Equation”, IFAC PAPERSONLINE, 51:32 (2018), 866–870
A. A. Uspenskii, P. D. Lebedev, “Evklidovo rasstoyanie do zamknutogo mnozhestva kak minimaksnoe reshenie zadachi Dirikhle dlya uravneniya Gamiltona-Yakobi”, Vestnik Tambovskogo universiteta. Seriya: estestvennye i tekhnicheskie nauki, 23:124 (2018), 797–804
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