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International Journal of Mathematics and Mathematical Sciences
Volume 18, Issue 3, Pages 601-605
http://dx.doi.org/10.1155/S0161171295000755

Surface temperature determination from Borehole measurements: Regularization and error estimates

1HoChiMinh City University, Department of Mathematics, HoChiMinh City, Vietnam
2University of the Philippines, Department of Mathematics, Diliman, Quezon City, Philippines

Received 15 July 1993; Revised 30 March 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Hα(), 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.