Solvability of the Gellerstedt problem with data on parallel characteristics
We study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with boundary conditions on parallel characteristics in the hyperbolic domain of the equation. Three distinct types of conditions on the type change lines are considered, and existence and uniqueness theorems for the corresponding...
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| Published in | Differential equations Vol. 53; no. 10; pp. 1346 - 1351 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Moscow
Pleiades Publishing
01.10.2017
Springer Nature B.V |
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| Abstract | We study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with boundary conditions on parallel characteristics in the hyperbolic domain of the equation. Three distinct types of conditions on the type change lines are considered, and existence and uniqueness theorems for the corresponding problems are proved. |
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| AbstractList | We study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with boundary conditions on parallel characteristics in the hyperbolic domain of the equation. Three distinct types of conditions on the type change lines are considered, and existence and uniqueness theorems for the corresponding problems are proved. |
| Author | Moiseev, T. E. Kholomeeva, A. A. Moiseev, E. I. |
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| Copyright | Pleiades Publishing, Ltd. 2017 Copyright Springer Science & Business Media Oct 2017 |
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| References | SmirnovM.M.Uravneniya smeshannogo tipa (Equations of the Mixed Type)1985 FranklF.I.New example of a plane-parallel transonic flow with a direct compression shock ending inside the flowIzv. Vyssh. Uchebn. Zaved. Mat.19592244246 MoiseevT.E.Gellerstedt problem with nonclassical matching conditions for the solution gradient on the type change line with data on internal characteristicsDiffer. Equations201652810231029355461110.1134/S00122661160800731357.35235 MoiseevE.I.On the basis property of a sine systemDiffer. Uravn.19872311771790645.42014 BitsadzeA.V.Nekotorye klassy uravnenii v chastnykh proizvodnykh (Some Classes of Partial Differential Equations)19810511.35001 MoiseevT.E.On the solution of the Gellerstedt problem for the Lavrent’ev–Bitsadze equationDiffer. Equations2012481014331435318013510.1134/S001226611210014X1330.35271 MoiseevE.I.Solution of the Tricomi problem in special domainsDiffer. Equations1990261839110503640702.35179 MoiseevT.E.Gellerstedt problem with a generalized Frankl matching condition on the type change line with data on external characteristicsDiffer. Equations2016522240247354019910.1134/S00122661160200991342.35186 T.E. Moiseev (572_CR7) 2012; 48 E.I. Moiseev (572_CR6) 1990; 26 T.E. Moiseev (572_CR5) 2016; 52 A.V. Bitsadze (572_CR1) 1981 M.M. Smirnov (572_CR2) 1985 E.I. Moiseev (572_CR8) 1987; 23 F.I. Frankl (572_CR3) 1959; 2 T.E. Moiseev (572_CR4) 2016; 52 |
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| Snippet | We study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with boundary conditions on parallel characteristics in the hyperbolic domain of the... |
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| SubjectTerms | Boundary conditions Difference and Functional Equations Differential equations Existence theorems Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Uniqueness theorems |
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| Title | Solvability of the Gellerstedt problem with data on parallel characteristics |
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