On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

Journal of inequalities and applications

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