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2 results on '"47A52, 20M17, 26D15"'

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

Author

Khoa, Vo Anh, Lan, Le Trong, Tuan, Nguyen Huy, and Hung, Tran The

Subjects
Mathematics - Analysis of PDEs, Mathematics - Functional Analysis, 47A52, 20M17, 26D15
Abstract

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 new 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 to the earlier results in Zouyed et al. \cite{key-9} (2014)., Comment: 19 pages, 4 figures, 1 table

Published
2014
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2. On the regularization of solution of an inverse ultraparabolic equation associated with perturbed final data

Author

Nguyen Huy Tuan, Vo Anh Khoa, Le Trong Lan, and Tran The Hung

Subjects
Applied Mathematics, Inverse, Inverse problem, 47A52, 20M17, 26D15, Regularization (mathematics), Instability, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, FOS: Mathematics, Applied mathematics, Discrete Mathematics and Combinatorics, Analysis, Mathematics, Analysis of PDEs (math.AP)
Abstract

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 new 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 to the earlier results in Zouyed et al. \cite{key-9} (2014)., 19 pages, 4 figures, 1 table

Full Text
View/download PDF

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