Tricomi problem and integral equations
Formulas for inverting integral equations that arise when studying the Tricomi problem for the Lavrentyev–Bitsadze equation were derived. Solvability conditions of an auxiliary overdetermined problem in the elliptic part of the mixed domain were found using the Green function method. A connection wa...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-04-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/40 |
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| _version_ | 1832543015941439488 |
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| author | N. B. Pleshchinskii |
| author_facet | N. B. Pleshchinskii |
| author_sort | N. B. Pleshchinskii |
| collection | DOAJ |
| description | Formulas for inverting integral equations that arise when studying the Tricomi problem for the Lavrentyev–Bitsadze equation were derived. Solvability conditions of an auxiliary overdetermined problem in the elliptic part of the mixed domain were found using the Green function method. A connection was established between the Green functions of the Dirichlet problem and problem N for the Laplace equation in the form of integral equations mutually inverting each other. Various integral equations were considered, including explicitly solvable ones, to which the Tricomi problem can be reduced. An explicit solution of the characteristic singular equation with a Cauchy kernel was obtained without involving the theory of boundary value problems for analytic functions. |
| format | Article |
| id | doaj-art-6818221b35fd4f9cb828bb3c0adaedde |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-6818221b35fd4f9cb828bb3c0adaedde2025-02-03T12:00:35ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-04-011661749110.26907/2541-7746.2024.1.74-9135Tricomi problem and integral equationsN. B. Pleshchinskii0Kazan Federal UniversityFormulas for inverting integral equations that arise when studying the Tricomi problem for the Lavrentyev–Bitsadze equation were derived. Solvability conditions of an auxiliary overdetermined problem in the elliptic part of the mixed domain were found using the Green function method. A connection was established between the Green functions of the Dirichlet problem and problem N for the Laplace equation in the form of integral equations mutually inverting each other. Various integral equations were considered, including explicitly solvable ones, to which the Tricomi problem can be reduced. An explicit solution of the characteristic singular equation with a Cauchy kernel was obtained without involving the theory of boundary value problems for analytic functions.https://uzakufismat.elpub.ru/jour/article/view/40tricomi problemoverdetermined problemintegral equationgreen functionconformal mapping |
| spellingShingle | N. B. Pleshchinskii Tricomi problem and integral equations Учёные записки Казанского университета: Серия Физико-математические науки tricomi problem overdetermined problem integral equation green function conformal mapping |
| title | Tricomi problem and integral equations |
| title_full | Tricomi problem and integral equations |
| title_fullStr | Tricomi problem and integral equations |
| title_full_unstemmed | Tricomi problem and integral equations |
| title_short | Tricomi problem and integral equations |
| title_sort | tricomi problem and integral equations |
| topic | tricomi problem overdetermined problem integral equation green function conformal mapping |
| url | https://uzakufismat.elpub.ru/jour/article/view/40 |
| work_keys_str_mv | AT nbpleshchinskii tricomiproblemandintegralequations |