To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations
We study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielliptic equations and equations of many other types....
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/3/487 |
| _version_ | 1797318476844498944 |
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| author | Aleksandr I. Kozhanov |
| author_facet | Aleksandr I. Kozhanov |
| author_sort | Aleksandr I. Kozhanov |
| collection | DOAJ |
| description | We study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielliptic equations and equations of many other types. For the above equations, the following theorems are proved with the use of the splitting method: the existence of regular solutions—solutions that all have weak derivatives in the sense of S. L. Sobolev and occur in the corresponding equation. |
| first_indexed | 2024-03-08T03:52:57Z |
| format | Article |
| id | doaj.art-a97ec3a6dbbb41c9863ced12ed57e6cb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-08T03:52:57Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a97ec3a6dbbb41c9863ced12ed57e6cb2024-02-09T15:18:31ZengMDPI AGMathematics2227-73902024-02-0112348710.3390/math12030487To the Question of the Solvability of the Ionkin Problem for Partial Differential EquationsAleksandr I. Kozhanov0Sobolev Institute of Mathematics, Acad. Koptyug, 4, Novosibirsk 630090, RussiaWe study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielliptic equations and equations of many other types. For the above equations, the following theorems are proved with the use of the splitting method: the existence of regular solutions—solutions that all have weak derivatives in the sense of S. L. Sobolev and occur in the corresponding equation.https://www.mdpi.com/2227-7390/12/3/487spatial nonlocal problemsIonkin conditionsplitting methodregular solutionsexistenceuniqueness |
| spellingShingle | Aleksandr I. Kozhanov To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations Mathematics spatial nonlocal problems Ionkin condition splitting method regular solutions existence uniqueness |
| title | To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations |
| title_full | To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations |
| title_fullStr | To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations |
| title_full_unstemmed | To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations |
| title_short | To the Question of the Solvability of the Ionkin Problem for Partial Differential Equations |
| title_sort | to the question of the solvability of the ionkin problem for partial differential equations |
| topic | spatial nonlocal problems Ionkin condition splitting method regular solutions existence uniqueness |
| url | https://www.mdpi.com/2227-7390/12/3/487 |
| work_keys_str_mv | AT aleksandrikozhanov tothequestionofthesolvabilityoftheionkinproblemforpartialdifferentialequations |