Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation
We consider a linear inverse problem for a second-order abstract differential equation in a Banach space. The inhomogeneous term of the equation does not depend on time and is unknown. At the initial moment of time, the standard Cauchy conditions are given. An additional condition is specified at th...
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Irkutsk State University
2024-12-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1506 |
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| author | M. Almohamed |
| author_facet | M. Almohamed |
| author_sort | M. Almohamed |
| collection | DOAJ |
| description | We consider a linear inverse problem for a second-order abstract differential equation in a Banach space. The inhomogeneous term of the equation does not depend on time and is unknown. At the initial moment of time, the standard Cauchy conditions are given. An additional condition is specified at the final moment of time. This is a value of the second derivative of the main evolutionary function. For the studied problem, a uniqueness criterion of a solution is established. It is expressed in spectral terms. A simple sufficient condition for the solution uniqueness is noted. An example of the inverse problem for Poisson’s equation in a cylindrical domain is considered. |
| format | Article |
| id | doaj-art-90f364f89e3b4d429bd73915bd22d2b1 |
| institution | Kabale University |
| issn | 1997-7670 2541-8785 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj-art-90f364f89e3b4d429bd73915bd22d2b12024-12-07T11:13:22ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852024-12-01501518https://doi.org/10.26516/1997-7670.2024.50.5Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential EquationM. AlmohamedWe consider a linear inverse problem for a second-order abstract differential equation in a Banach space. The inhomogeneous term of the equation does not depend on time and is unknown. At the initial moment of time, the standard Cauchy conditions are given. An additional condition is specified at the final moment of time. This is a value of the second derivative of the main evolutionary function. For the studied problem, a uniqueness criterion of a solution is established. It is expressed in spectral terms. A simple sufficient condition for the solution uniqueness is noted. An example of the inverse problem for Poisson’s equation in a cylindrical domain is considered.https://mathizv.isu.ru/en/article/file?id=1506abstract differential equation of the second orderlinear inverse problemuniqueness criterion of solutionelementary solutions of inverse problem |
| spellingShingle | M. Almohamed Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation Известия Иркутского государственного университета: Серия "Математика" abstract differential equation of the second order linear inverse problem uniqueness criterion of solution elementary solutions of inverse problem |
| title | Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation |
| title_full | Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation |
| title_fullStr | Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation |
| title_full_unstemmed | Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation |
| title_short | Uniqueness of Solution of the Inverse Problem with Overdetermination of the Raised Type for an Abstract Second-order Differential Equation |
| title_sort | uniqueness of solution of the inverse problem with overdetermination of the raised type for an abstract second order differential equation |
| topic | abstract differential equation of the second order linear inverse problem uniqueness criterion of solution elementary solutions of inverse problem |
| url | https://mathizv.isu.ru/en/article/file?id=1506 |
| work_keys_str_mv | AT malmohamed uniquenessofsolutionoftheinverseproblemwithoverdeterminationoftheraisedtypeforanabstractsecondorderdifferentialequation |