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

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• 作者：Nguyen Huy Tuan (1)
  Vo Anh Khoa (2) (3)
  Le Trong Lan (3)
  Tran The Hung (3)
  
  1. Applied Analysis Research Group ; Faculty of Mathematics and Statistics ; Ton Duc Thang University ; Ho Chi Minh City ; Vietnam
  2. Mathematics and Computer Science Division ; Gran Sasso Science Institute ; Viale Francesco Crispi 7 ; L鈥橝quila ; Abruzzo ; 67100 ; Italy
  3. Department of Mathematics and Computer Science ; Ho Chi Minh City University of Science ; 227 Nguyen Van Cu Street ; District 5 ; Ho Chi Minh City ; Vietnam
  
• 关键词：47A52 ; 20M17 ; 26D15 ; ultraparabolic equation ; ill ; posed problem ; semi ; group method ; stability ; error estimate
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,293 KB
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• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

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).