Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities
We investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. Thi...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/6/424 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849467406190116864 |
|---|---|
| author | Zülal Mısır Metin Yaman |
| author_facet | Zülal Mısır Metin Yaman |
| author_sort | Zülal Mısır |
| collection | DOAJ |
| description | We investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. This class of inverse problems, where internal terms such as source and damping are to be determined from indirect measurements, has significant relevance in real-world applications—ranging from geophysical prospecting to biomedical engineering and materials science. The accurate identification of these internal mechanisms plays a crucial role in optimizing system performance, improving diagnostic accuracy, and constructing predictive models. Therefore, the results obtained in this study not only contribute to the theoretical understanding of nonlinear dynamic systems but also provide practical insights for reconstructive analysis and control in applied settings. The asymptotic behavior and decay conditions we derive are expected to be of particular interest to researchers dealing with stability, uniqueness, and identifiability in inverse problems governed by nonstandard growth conditions. |
| format | Article |
| id | doaj-art-e3fe1942c3d54c49923883c4b8f8a4e6 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-e3fe1942c3d54c49923883c4b8f8a4e62025-08-20T03:26:15ZengMDPI AGAxioms2075-16802025-05-0114642410.3390/axioms14060424Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent NonlinearitiesZülal Mısır0Metin Yaman1Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, TurkeyDepartment of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, TurkeyWe investigate an inverse problem involving source and damping term with variable-exponent nonlinearities. We establish adequate conditions on the initial data for the decay of solutions as the integral overdetermination approaches zero over time within an acceptable range of variable exponents. This class of inverse problems, where internal terms such as source and damping are to be determined from indirect measurements, has significant relevance in real-world applications—ranging from geophysical prospecting to biomedical engineering and materials science. The accurate identification of these internal mechanisms plays a crucial role in optimizing system performance, improving diagnostic accuracy, and constructing predictive models. Therefore, the results obtained in this study not only contribute to the theoretical understanding of nonlinear dynamic systems but also provide practical insights for reconstructive analysis and control in applied settings. The asymptotic behavior and decay conditions we derive are expected to be of particular interest to researchers dealing with stability, uniqueness, and identifiability in inverse problems governed by nonstandard growth conditions.https://www.mdpi.com/2075-1680/14/6/424decay of solutionelasticity termvariable exponentinverse problemgeneral decayLamé equation |
| spellingShingle | Zülal Mısır Metin Yaman Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities Axioms decay of solution elasticity term variable exponent inverse problem general decay Lamé equation |
| title | Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities |
| title_full | Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities |
| title_fullStr | Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities |
| title_full_unstemmed | Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities |
| title_short | Decay Estimates for a Lamé Inverse Problem Involving Source and Damping Term with Variable-Exponent Nonlinearities |
| title_sort | decay estimates for a lame inverse problem involving source and damping term with variable exponent nonlinearities |
| topic | decay of solution elasticity term variable exponent inverse problem general decay Lamé equation |
| url | https://www.mdpi.com/2075-1680/14/6/424 |
| work_keys_str_mv | AT zulalmısır decayestimatesforalameinverseprobleminvolvingsourceanddampingtermwithvariableexponentnonlinearities AT metinyaman decayestimatesforalameinverseprobleminvolvingsourceanddampingtermwithvariableexponentnonlinearities |