ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS
In this paper, we first prove that the heat equation backward in time with Dirichlet and integral boundary conditions is an ill- posed problem. Then, we establish a stability estimate of Hölder type for this ill-posed problem.
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| Format: | Article |
| Language: | English |
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Trường Đại học Vinh
2024-12-01
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| Series: | Tạp chí Khoa học |
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| Online Access: | https://vujs.vn//api/view.aspx?cid=0f8ac6a3-6adc-4aa4-8a96-375354133650 |
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| _version_ | 1841550796372574208 |
|---|---|
| author | Nguyen Van Duc Phan Hoai Linh |
| author_facet | Nguyen Van Duc Phan Hoai Linh |
| author_sort | Nguyen Van Duc |
| collection | DOAJ |
| description | In this paper, we first prove that the heat equation backward in
time with Dirichlet and integral boundary conditions is an ill-
posed problem. Then, we establish a stability estimate of Hölder
type for this ill-posed problem. |
| format | Article |
| id | doaj-art-c0ad32c45f3f4ac6928e8c711107395e |
| institution | Kabale University |
| issn | 1859-2228 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Trường Đại học Vinh |
| record_format | Article |
| series | Tạp chí Khoa học |
| spelling | doaj-art-c0ad32c45f3f4ac6928e8c711107395e2025-01-10T03:32:37ZengTrường Đại học VinhTạp chí Khoa học1859-22282024-12-01534A909810.56824/vujs.2024a079aILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONSNguyen Van Duc0Phan Hoai Linh1Department of Mathematics, Vinh University, Nghe An, VietnamMaster's student course 30, Analytical Mathematics, Department of Mathematics, Vinh University, Nghe An, VietnamIn this paper, we first prove that the heat equation backward in time with Dirichlet and integral boundary conditions is an ill- posed problem. Then, we establish a stability estimate of Hölder type for this ill-posed problem.https://vujs.vn//api/view.aspx?cid=0f8ac6a3-6adc-4aa4-8a96-375354133650heat equation backwardill-posed problemstability estimate |
| spellingShingle | Nguyen Van Duc Phan Hoai Linh ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS Tạp chí Khoa học heat equation backward ill-posed problem stability estimate |
| title | ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS |
| title_full | ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS |
| title_fullStr | ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS |
| title_full_unstemmed | ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS |
| title_short | ILL-POSEDNESS AND STABILITY ESTIMATE FOR THE HEAT EQUATION BACKWARD IN TIME WITH DIRICHLET AND INTEGRAL BOUNDARY CONDITIONS |
| title_sort | ill posedness and stability estimate for the heat equation backward in time with dirichlet and integral boundary conditions |
| topic | heat equation backward ill-posed problem stability estimate |
| url | https://vujs.vn//api/view.aspx?cid=0f8ac6a3-6adc-4aa4-8a96-375354133650 |
| work_keys_str_mv | AT nguyenvanduc illposednessandstabilityestimatefortheheatequationbackwardintimewithdirichletandintegralboundaryconditions AT phanhoailinh illposednessandstabilityestimatefortheheatequationbackwardintimewithdirichletandintegralboundaryconditions |