Electron. J. Differential Equations, Vol. 2016 (2016), No. 256, pp. 1-12.

Regularization and error estimates for asymmetric backward nonhomogeneous heat equations in a ball

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
email: leminhtriet@tdt.edu.vn
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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