Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$
In this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi)$. We obtain an approximated solution using the Fo...
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| Format: | Article |
| Language: | English |
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Qom University of Technology
2023-03-01
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| Series: | Mathematics and Computational Sciences |
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| Online Access: | https://mcs.qut.ac.ir/article_703893_d21afa1d1e996a0c865b31213980d906.pdf |
| _version_ | 1827307657394913280 |
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| author | Phong Tran Long Le |
| author_facet | Phong Tran Long Le |
| author_sort | Phong Tran |
| collection | DOAJ |
| description | In this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi)$. We obtain an approximated solution using the Fourier method and the final input data $L^{r}(0,\pi)$ for $r \neq 2$. Using embedding between $L^{r}(0,\pi)$ and Hilbert scales $\mathcal{H}^{\rho}(0,\pi)$, this study is the error between the exact and regularized solutions to be estimated in $L^{r}(0,\pi)$. |
| first_indexed | 2024-03-08T05:36:01Z |
| format | Article |
| id | doaj.art-88721425ded14841b77322cb83af7586 |
| institution | Directory Open Access Journal |
| issn | 2717-2708 |
| language | English |
| last_indexed | 2024-04-24T18:43:18Z |
| publishDate | 2023-03-01 |
| publisher | Qom University of Technology |
| record_format | Article |
| series | Mathematics and Computational Sciences |
| spelling | doaj.art-88721425ded14841b77322cb83af75862024-03-27T09:02:54ZengQom University of TechnologyMathematics and Computational Sciences2717-27082023-03-0141455710.30511/mcs.2023.1990393.1111703893Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$Phong Tran0Long Le1Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, VietnamDivision of Applied Mathematics, Science and Technology Advanced Institute Van Lang University, Ho Chi Minh City, Viet NamIn this work, we focus on the final value problem of an inverse problem for the pseudo-parabolic equation. This study aims to provide a regularization method for this equation, once the measurement data are obtained at the final time in $L^{r}(0,\pi)$. We obtain an approximated solution using the Fourier method and the final input data $L^{r}(0,\pi)$ for $r \neq 2$. Using embedding between $L^{r}(0,\pi)$ and Hilbert scales $\mathcal{H}^{\rho}(0,\pi)$, this study is the error between the exact and regularized solutions to be estimated in $L^{r}(0,\pi)$.https://mcs.qut.ac.ir/article_703893_d21afa1d1e996a0c865b31213980d906.pdfsource problemfractional pseudo-parabolic problemill-posed problemconvergence estimatesregularization |
| spellingShingle | Phong Tran Long Le Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ Mathematics and Computational Sciences source problem fractional pseudo-parabolic problem ill-posed problem convergence estimates regularization |
| title | Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ |
| title_full | Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ |
| title_fullStr | Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ |
| title_full_unstemmed | Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ |
| title_short | Approximation of inverse source problem for time fractional pseudo-parabolic equation in $L^p$ |
| title_sort | approximation of inverse source problem for time fractional pseudo parabolic equation in l p |
| topic | source problem fractional pseudo-parabolic problem ill-posed problem convergence estimates regularization |
| url | https://mcs.qut.ac.ir/article_703893_d21afa1d1e996a0c865b31213980d906.pdf |
| work_keys_str_mv | AT phongtran approximationofinversesourceproblemfortimefractionalpseudoparabolicequationinlp AT longle approximationofinversesourceproblemfortimefractionalpseudoparabolicequationinlp |