Solvability conditions for three-point problem for a partial differential equation in two-dimensional cylinder
The paper deals with the investigation of a three-point problem for a partial differential equation in a two-dimensional domain. We estab\-lish sufficient conditions for the existence of a solution to this problem and sufficient and necessary conditions for the uniqueness of the solution in the corr...
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| Date: | 2015 |
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| Author Affiliations: |
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| Keywords: | keywords |
| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2015
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/123 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | The paper deals with the investigation of a three-point problem for a partial differential equation in a two-dimensional domain. We estab\-lish sufficient conditions for the existence of a solution to this problem and sufficient and necessary conditions for the uniqueness of the solution in the corresponding weighted Sobolev spaces (Abel spaces). A similar problem for an equation in several spatial variables is ill-posed in the sense of Hadamard; its solvability is connected with the problem of small denominators, which arises in the construction of the solution. In the case of a single spatial variable we estimate the corresponding denominators by constants and show that the problem is well-posed in the sense of Hadamard in the Abel spaces. |
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