Le Minh Triet, Luu Hong Phong
Abstract:
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.
Show me the PDF file (322 KB), TEX file for this article.
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Le Minh Triet Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City, Vietnam email: leminhtriet@tdt.edu.vn |
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Luu Hong Phong Faculty of Mathematics University of Science Vietnam National University Ho chi Minh city, Vietnam email: luuhongphong2812@gmail.com |
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