International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 601-605
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 Tran Thi Le and Milagros Navarro. 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.
The authors consider the problem of determining the temperature distribution on
the half-line , , from measurements at an interior point, for all . 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 , . They give an error estimate of the order
for , where is a bound on the measurement error.