Uniqueness for a boundary identification problem in thermal imaging
An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in ${mathbb R}^n$ from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differen...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
1998-11-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/01/b2/abstr.html |
| _version_ | 1818562660043587584 |
|---|---|
| author | Kurt Bryan Lester F. Caudill Jr. |
| author_facet | Kurt Bryan Lester F. Caudill Jr. |
| author_sort | Kurt Bryan |
| collection | DOAJ |
| description | An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in ${mathbb R}^n$ from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs. |
| first_indexed | 2024-12-14T01:06:41Z |
| format | Article |
| id | doaj.art-509bb4eb59a5407bb78e868c84e00c48 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:06:41Z |
| publishDate | 1998-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-509bb4eb59a5407bb78e868c84e00c482022-12-21T23:22:57ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911998-11-01Conference012339Uniqueness for a boundary identification problem in thermal imagingKurt BryanLester F. Caudill Jr.An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in ${mathbb R}^n$ from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs.http://ejde.math.txstate.edu/conf-proc/01/b2/abstr.htmlInverse problemsnon-destructive testingthermal imaging. |
| spellingShingle | Kurt Bryan Lester F. Caudill Jr. Uniqueness for a boundary identification problem in thermal imaging Electronic Journal of Differential Equations Inverse problems non-destructive testing thermal imaging. |
| title | Uniqueness for a boundary identification problem in thermal imaging |
| title_full | Uniqueness for a boundary identification problem in thermal imaging |
| title_fullStr | Uniqueness for a boundary identification problem in thermal imaging |
| title_full_unstemmed | Uniqueness for a boundary identification problem in thermal imaging |
| title_short | Uniqueness for a boundary identification problem in thermal imaging |
| title_sort | uniqueness for a boundary identification problem in thermal imaging |
| topic | Inverse problems non-destructive testing thermal imaging. |
| url | http://ejde.math.txstate.edu/conf-proc/01/b2/abstr.html |
| work_keys_str_mv | AT kurtbryan uniquenessforaboundaryidentificationprobleminthermalimaging AT lesterfcaudilljr uniquenessforaboundaryidentificationprobleminthermalimaging |