Journal of inequalities and applications | |
On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data | |
Nguyen Huy Tuan1  | |
关键词: ultraparabolic equation; ill-posed problem; semi-group method; stability; error estimate; 47A52; 20M17; 26D15; | |
DOI : 10.1186/s13660-014-0526-y | |
学科分类:数学(综合) | |
来源: SpringerOpen | |
【 摘 要 】
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the instability cause. Since the solution exhibits unstable dependence on the given data functions, we propose a regularization method to stabilize the solution, then obtain the error estimate. A numerical example shows that the method is efficient and feasible. This work slightly extends the earlier results in Zouyed and Rebbani (J. Inverse Ill-Posed Probl. 22(4):449-466, 2014).
【 授权许可】
CC BY
【 预 览 】
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RO201902019571171ZK.pdf | 1293KB | download |