Convergence rates for Tikhonov regularization of a coefficient identification problem

This paper investigates the convergence rates for Tikhonov regularization of the problem for identifying the coefficient in the frequency-domain acoustic wave equation in general dimensional spaces; here , , and . We assume that we know the imprecise measurement data of 𝑢 in the subdomain with a mea...

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Bibliographic Details
Published inJournal of inverse and ill-posed problems Vol. 33; no. 4; pp. 497 - 513
Main Authors Huang, Huimin, Zhang, Wensheng
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.08.2025
Walter de Gruyter GmbH
Subjects
35L05
35R25
35R30
47A52
49N45
Acoustic waves
Boundary conditions
Coefficient identification
Convergence
convergence rate
functional
Regularization
Tikhonov solution
wave equation
Wave equations
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Summary:This paper investigates the convergence rates for Tikhonov regularization of the problem for identifying the coefficient in the frequency-domain acoustic wave equation in general dimensional spaces; here , , and . We assume that we know the imprecise measurement data of 𝑢 in the subdomain with a measurement error of level , while 𝑢 satisfies the general Robin boundary condition on . We propose to regularize this problem by minimizing a new functional and prove that the functional attains a unique global minimum on the admissible set of . Furthermore, we derive the convergence rate for the Tikhonov regularized solution with an easily satisfied source condition.
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content type line 14
ISSN:0928-0219
1569-3945
DOI:10.1515/jiip-2024-0057