On recovering parabolic diffusions from their time-averages
The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that t...
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| Format: | Journal Article |
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Springer Nature
2019
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| Online Access: | http://hdl.handle.net/20.500.11937/75202 |
| _version_ | 1848763453679861760 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that this new problem is well-posed in certain classes of solutions. The paper establishes existence, uniqueness, and a regularity of the solution for this new problem and its modifications, including problems with singled out terminal values. |
| first_indexed | 2025-11-14T11:03:42Z |
| format | Journal Article |
| id | curtin-20.500.11937-75202 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:03:42Z |
| publishDate | 2019 |
| publisher | Springer Nature |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-752022020-01-06T08:38:59Z On recovering parabolic diffusions from their time-averages Dokuchaev, Nikolai The paper study a possibility to recover a parabolic diffusion from its time-average when the values at the initial time are unknown. This problem can be reformulated as a new boundary value problem where a Cauchy condition is replaced by a prescribed time-average of the solution. It is shown that this new problem is well-posed in certain classes of solutions. The paper establishes existence, uniqueness, and a regularity of the solution for this new problem and its modifications, including problems with singled out terminal values. 2019 Journal Article http://hdl.handle.net/20.500.11937/75202 10.1007/s00526-018-1464-1 Springer Nature fulltext |
| spellingShingle | Dokuchaev, Nikolai On recovering parabolic diffusions from their time-averages |
| title | On recovering parabolic diffusions from their time-averages |
| title_full | On recovering parabolic diffusions from their time-averages |
| title_fullStr | On recovering parabolic diffusions from their time-averages |
| title_full_unstemmed | On recovering parabolic diffusions from their time-averages |
| title_short | On recovering parabolic diffusions from their time-averages |
| title_sort | on recovering parabolic diffusions from their time-averages |
| url | http://hdl.handle.net/20.500.11937/75202 |