Inverse problem for an abstract neutral differential equation of Sobolev-type
In this manuscript, we consider an inverse problem for the neutral differential equation of Sobolev type with a deviated argument and identify the parameter using an overdetermined condition on a mild solution. A direct approach using Volterra integral equations for sufficiently regular data and an...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Results in Control and Optimization |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720723000371 |
| _version_ | 1797802735001665536 |
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| author | Muslim Malik Santosh Ruhil |
| author_facet | Muslim Malik Santosh Ruhil |
| author_sort | Muslim Malik |
| collection | DOAJ |
| description | In this manuscript, we consider an inverse problem for the neutral differential equation of Sobolev type with a deviated argument and identify the parameter using an overdetermined condition on a mild solution. A direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the result. Under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original inverse problem under specific hypotheses. At last, an example is provided in the support of our results. |
| first_indexed | 2024-03-13T05:10:12Z |
| format | Article |
| id | doaj.art-aeb8c52406bb41fe8abf932c6c2c3c63 |
| institution | Directory Open Access Journal |
| issn | 2666-7207 |
| language | English |
| last_indexed | 2024-03-13T05:10:12Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj.art-aeb8c52406bb41fe8abf932c6c2c3c632023-06-16T05:11:57ZengElsevierResults in Control and Optimization2666-72072023-06-0111100235Inverse problem for an abstract neutral differential equation of Sobolev-typeMuslim Malik0Santosh Ruhil1School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Mandi 175005, IndiaCorresponding author.; School of Mathematical and Statistical Sciences, Indian Institute of Technology Mandi, Mandi 175005, IndiaIn this manuscript, we consider an inverse problem for the neutral differential equation of Sobolev type with a deviated argument and identify the parameter using an overdetermined condition on a mild solution. A direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the result. Under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original inverse problem under specific hypotheses. At last, an example is provided in the support of our results.http://www.sciencedirect.com/science/article/pii/S2666720723000371Inverse problemsSobolev type differential equationsNeutral differential equationVolterra integral equationOptimal control |
| spellingShingle | Muslim Malik Santosh Ruhil Inverse problem for an abstract neutral differential equation of Sobolev-type Results in Control and Optimization Inverse problems Sobolev type differential equations Neutral differential equation Volterra integral equation Optimal control |
| title | Inverse problem for an abstract neutral differential equation of Sobolev-type |
| title_full | Inverse problem for an abstract neutral differential equation of Sobolev-type |
| title_fullStr | Inverse problem for an abstract neutral differential equation of Sobolev-type |
| title_full_unstemmed | Inverse problem for an abstract neutral differential equation of Sobolev-type |
| title_short | Inverse problem for an abstract neutral differential equation of Sobolev-type |
| title_sort | inverse problem for an abstract neutral differential equation of sobolev type |
| topic | Inverse problems Sobolev type differential equations Neutral differential equation Volterra integral equation Optimal control |
| url | http://www.sciencedirect.com/science/article/pii/S2666720723000371 |
| work_keys_str_mv | AT muslimmalik inverseproblemforanabstractneutraldifferentialequationofsobolevtype AT santoshruhil inverseproblemforanabstractneutraldifferentialequationofsobolevtype |