Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball
The backward heat problem (BHP) has been researched by many authors in the last five decades; it consists in recovering the initial distribution from the final temperature data. There are some articles [1,2,3] related the axi-symmetric BHP in a disk but the study in spherical coordinates is rare...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-09-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/256/abstr.html |
| _version_ | 1818062506741989376 |
|---|---|
| author | Le Minh Triet Luu Hong Phong |
| author_facet | Le Minh Triet Luu Hong Phong |
| author_sort | Le Minh Triet |
| collection | DOAJ |
| description | The backward heat problem (BHP) has been researched by many
authors in the last five decades; it consists in recovering the initial
distribution from the final temperature data.
There are some articles [1,2,3] related the axi-symmetric BHP in
a disk but the study in spherical coordinates is rare. Therefore, we wish to
study a backward problem for nonhomogenous heat equation associated with
asymmetric final data in a ball. In this article, we modify the
quasi-boundary value method to construct a stable approximate solution
for this problem. As a result, we obtain regularized solution and a sharp
estimates for its error. At the end, a numerical
experiment is provided to illustrate our method. |
| first_indexed | 2024-12-10T14:05:18Z |
| format | Article |
| id | doaj.art-3495d3509f524d219e73576dc37b4472 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T14:05:18Z |
| publishDate | 2016-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3495d3509f524d219e73576dc37b44722022-12-22T01:45:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-09-012016256,112Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ballLe Minh Triet0Luu Hong Phong1 Ton Duc Thang Univ. Ho Chi Minh City, Vietnam Vietnam National Univ., Ho chi Minh city, Vietnam The backward heat problem (BHP) has been researched by many authors in the last five decades; it consists in recovering the initial distribution from the final temperature data. There are some articles [1,2,3] related the axi-symmetric BHP in a disk but the study in spherical coordinates is rare. Therefore, we wish to study a backward problem for nonhomogenous heat equation associated with asymmetric final data in a ball. In this article, we modify the quasi-boundary value method to construct a stable approximate solution for this problem. As a result, we obtain regularized solution and a sharp estimates for its error. At the end, a numerical experiment is provided to illustrate our method.http://ejde.math.txstate.edu/Volumes/2016/256/abstr.htmlBackward heat problemquasi-boundary value methodspherical coordinatesill-posed problem |
| spellingShingle | Le Minh Triet Luu Hong Phong Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball Electronic Journal of Differential Equations Backward heat problem quasi-boundary value method spherical coordinates ill-posed problem |
| title | Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| title_full | Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| title_fullStr | Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| title_full_unstemmed | Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| title_short | Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| title_sort | regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball |
| topic | Backward heat problem quasi-boundary value method spherical coordinates ill-posed problem |
| url | http://ejde.math.txstate.edu/Volumes/2016/256/abstr.html |
| work_keys_str_mv | AT leminhtriet regularizationanderrorestimatesforasymmetricbackwardnonhomogeneousheatequationsinaball AT luuhongphong regularizationanderrorestimatesforasymmetricbackwardnonhomogeneousheatequationsinaball |