Geodesic
The solution of the problem of determining the density of heat sources in a rod
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 309-314 
A. A. Khromov; G. V. Khromova. The solution of the problem of determining the density of heat sources in a rod. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 3, pp. 309-314. http://geodesic.mathdoc.fr/item/ISU_2015_15_3_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known. First using the so-called discontinuous Steklov operator we construct families of operators which give stable uniform approximations to a function and its first and second derivatives, and then with their help we propose the method of solving the formulated problem. For a certain class of solutions error estimations are given.

[1] Ivanov V. K., Vasin V. V., Tanana V. P., The theory of linear ill-posed problems and its applications, Nauka, M., 1978, 206 pp. (in Russian) | MR

[2] Denisov A. M., Introduction to the theory of inverse problems, Moscow Univ. Press, M., 1994, 206 pp. (in Russian)

[3] Khromov A. A., “Approximation of Function and Its Derivative by the Modificated Steklov Operator”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:4(2) (2014), 595–599 (in Russian) | MR