Surface temperature determination from Borehole measurements: Regularization and error estimates
The authors consider the problem of determining the temperature distribution u(x,t) on the half-line x=0, t>0, from measurements at an interior point, for all t>0. As is well-known, this is an ill-posed problem Using the Tikhonov method, the authors give a regularized solution, and assuming th...
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Hindawi Limited
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000755 |
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doaj-72e421697ca7426b9a2e7822df820a742020-11-24T22:40:36ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118360160510.1155/S0161171295000755Surface temperature determination from Borehole measurements: Regularization and error estimatesTran Thi Le0Milagros Navarro1HoChiMinh City University, Department of Mathematics, HoChiMinh City, VietnamUniversity of the Philippines, Department of Mathematics, Diliman, Quezon City, PhilippinesThe authors consider the problem of determining the temperature distribution u(x,t) on the half-line x=0, t>0, from measurements at an interior point, for all t>0. As is well-known, this is an ill-posed problem Using the Tikhonov method, the authors give a regularized solution, and assuming the (unknown) exact solution is in Hα(ℝ), α>0. They give an error estimate of the order 1/(1n1/ ϵ )α for ϵ →0, where ϵ >0 is a bound on the measurement error.http://dx.doi.org/10.1155/S0161171295000755surface temperature distributionTikhonov regularizationerror estimate. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tran Thi Le Milagros Navarro |
| spellingShingle |
Tran Thi Le Milagros Navarro Surface temperature determination from Borehole measurements: Regularization and error estimates International Journal of Mathematics and Mathematical Sciences surface temperature distribution Tikhonov regularization error estimate. |
| author_facet |
Tran Thi Le Milagros Navarro |
| author_sort |
Tran Thi Le |
| title |
Surface temperature determination from Borehole measurements: Regularization and error estimates |
| title_short |
Surface temperature determination from Borehole measurements: Regularization and error estimates |
| title_full |
Surface temperature determination from Borehole measurements: Regularization and error estimates |
| title_fullStr |
Surface temperature determination from Borehole measurements: Regularization and error estimates |
| title_full_unstemmed |
Surface temperature determination from Borehole measurements: Regularization and error estimates |
| title_sort |
surface temperature determination from borehole measurements: regularization and error estimates |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1995-01-01 |
| description |
The authors consider the problem of determining the temperature distribution u(x,t) on
the half-line x=0, t>0, from measurements at an interior point, for all t>0. As is well-known, this is
an ill-posed problem Using the Tikhonov method, the authors give a regularized solution, and assuming
the (unknown) exact solution is in Hα(ℝ), α>0. They give an error estimate of the order 1/(1n1/ ϵ )α
for ϵ →0, where ϵ >0 is a bound on the measurement error. |
| topic |
surface temperature distribution Tikhonov regularization error estimate. |
| url |
http://dx.doi.org/10.1155/S0161171295000755 |
| work_keys_str_mv |
AT tranthile surfacetemperaturedeterminationfromboreholemeasurementsregularizationanderrorestimates AT milagrosnavarro surfacetemperaturedeterminationfromboreholemeasurementsregularizationanderrorestimates |
| _version_ |
1725704279407198208 |