Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term
The main goal of the paper is to approximate two types of inverse problems for conformable heat equation (or called parabolic equation with conformable operator); as follows, we considered two cases: the right hand side of equation such that Fx,t and Fx,t=φtfx. Up to now, there are very few surveys...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/8008838 |
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| author | L. D. Long Reza Saadati |
| author_facet | L. D. Long Reza Saadati |
| author_sort | L. D. Long |
| collection | DOAJ |
| description | The main goal of the paper is to approximate two types of inverse problems for conformable heat equation (or called parabolic equation with conformable operator); as follows, we considered two cases: the right hand side of equation such that Fx,t and Fx,t=φtfx. Up to now, there are very few surveys working on the results of regularization in Lp spaces. Our paper is the first work to investigate the inverse problem for conformable parabolic equations in such spaces. For the inverse source problem and the backward problem, use the Fourier truncation method to approximate the problem. The error between the regularized solution and the exact solution is obtained in Lp under some suitable assumptions on the Cauchy data. |
| format | Article |
| id | doaj-art-7d079e4b45ac40e0ab1fe3633854b1e9 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-7d079e4b45ac40e0ab1fe3633854b1e92025-02-03T06:08:46ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/8008838Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous TermL. D. Long0Reza Saadati1Division of Applied MathematicsSchool of MathematicsThe main goal of the paper is to approximate two types of inverse problems for conformable heat equation (or called parabolic equation with conformable operator); as follows, we considered two cases: the right hand side of equation such that Fx,t and Fx,t=φtfx. Up to now, there are very few surveys working on the results of regularization in Lp spaces. Our paper is the first work to investigate the inverse problem for conformable parabolic equations in such spaces. For the inverse source problem and the backward problem, use the Fourier truncation method to approximate the problem. The error between the regularized solution and the exact solution is obtained in Lp under some suitable assumptions on the Cauchy data.http://dx.doi.org/10.1155/2022/8008838 |
| spellingShingle | L. D. Long Reza Saadati Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term Journal of Function Spaces |
| title | Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term |
| title_full | Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term |
| title_fullStr | Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term |
| title_full_unstemmed | Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term |
| title_short | Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term |
| title_sort | regularization of inverse initial problem for conformable pseudo parabolic equation with inhomogeneous term |
| url | http://dx.doi.org/10.1155/2022/8008838 |
| work_keys_str_mv | AT ldlong regularizationofinverseinitialproblemforconformablepseudoparabolicequationwithinhomogeneousterm AT rezasaadati regularizationofinverseinitialproblemforconformablepseudoparabolicequationwithinhomogeneousterm |