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

Authors: 

Le Minh Triet, Luu Hong Phong

Source title: 
Electronic Journal of Differential Equations, 256: 1-12, 2016 (ISI)
Academic year of acceptance: 
2016-2017
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.