Surface temperature determination from Borehole measurements: Regularization and error estimates

Tran Thi Le and Milagros Navarro

International Journal of Mathematics and Mathematical Sciences, 1995, vol. 18, 1-5

Abstract:

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 H α ( ℝ ) , α > 0 . They give an error estimate of the order 1 / ( 1 n 1 / ϵ ) α for ϵ → 0 , where ϵ > 0 is a bound on the measurement error.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:730287

DOI: 10.1155/S0161171295000755

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