Le Minh Triet, Luu Hong Phong
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.
Submitted September 2, 2016. Published September 21, 2016.
Math Subject Classifications: 35R25, 35R30, 65M30.
Key Words: Backward heat problem; quasi-boundary value method; spherical coordinates; ill-posed problem.
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| Le Minh Triet |
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh City, Vietnam
| Luu Hong Phong |
Faculty of Mathematics
University of Science
Vietnam National University
Ho chi Minh city, Vietnam
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