Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions
This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization so...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2022-12, Vol.38 (12), p.2199-2219 |
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| container_issue | 12 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Phuong, Nguyen Duc Long, Le Dinh Nguyen, Anh Tuan Baleanu, Dumitru |
| description | This paper is devoted to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. First, we prove the problem is non-well posed and the stability of the source function. Second, by using the Modified Fractional Landweber method, we present regularization solutions and show the convergence rate between regularization solutions and sought solution are given under a priori and a posteriori choice rules of the regularization parameter, respectively. Finally, we present an illustrative numerical example to test the results of our theory. |
| doi_str_mv | 10.1007/s10114-022-1234-z |
| format | Article |
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Finally, we present an illustrative numerical example to test the results of our theory.</description><subject>Differential equations</subject><subject>Ill posed problems</subject><subject>Inverse problems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Regularization</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLwzAYhoMoOKc_wFvAczRJm6Y9yth0MHTIPIckTbaMrtmSVnG_3owOPHnKR3iel-97Abgn-JFgzJ8iwYTkCFOKCM1ydLwAI5JnFeIF4ZfnuWSkuAY3MW4xZqzCxQj0H2bdNzK4o-ycb6G3sNsYOG-_TIgGLoNXjdlB6wNcuZ2BsyD1CZQNXEbT1x7tZZDKN07D6aEfQr5dt4FvvkWN1wl07eBOfFu7ExBvwZWVTTR353cMPmfT1eQVLd5f5pPnBdIZKTpEKpWls0qWa8VVZVmpcyVVjimzPP1IpqWprcmq0uQG07KyRa2pxIqoTKo6G4OHIXcf_KE3sRNb34e0fBSUF5wVFaE8UWSgdPAxBmPFPridDD-CYHFqVwztitSuOLUrjsmhgxMT265N-Ev-X_oFJdl_mQ</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Phuong, Nguyen Duc</creator><creator>Long, Le Dinh</creator><creator>Nguyen, Anh Tuan</creator><creator>Baleanu, Dumitru</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20221201</creationdate><title>Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions</title><author>Phuong, Nguyen Duc ; Long, Le Dinh ; Nguyen, Anh Tuan ; Baleanu, Dumitru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-19b3011854cb7b9f58c4bab4025f7b7ba5caedfe398e4e0289f6dc2a0b1b3abd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Differential equations</topic><topic>Ill posed problems</topic><topic>Inverse problems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Regularization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Phuong, Nguyen Duc</creatorcontrib><creatorcontrib>Long, Le Dinh</creatorcontrib><creatorcontrib>Nguyen, Anh Tuan</creatorcontrib><creatorcontrib>Baleanu, Dumitru</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta mathematica Sinica. 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| subjects | Differential equations Ill posed problems Inverse problems Mathematics Mathematics and Statistics Regularization |
| title | Regularization of the Inverse Problem for Time Fractional Pseudo-parabolic Equation with Non-local in Time Conditions |
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