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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000755 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |