Retrospective task for a non-stationary operator of heat conductivity

1Panin, VV, 1Krivoshey, FA, 1Bogdan, Yu.A
1Hetman Petro Konashevich-Sahaydachniy Kyiv State Maritime Academy
Dopov. Nac. akad. nauk Ukr. 2014, 8:72-76
https://doi.org/10.15407/dopovidi2014.08.072
Section: Heat Physics
Language: Russian
Abstract: 

The limit case of a retrospective task of non-stationary heat conductivity (namely, the restoration of the initial distribution of temperatures) is considered. The need for it can arise at expert estimates of the thermal prehistory of an object, for example, an internal combustion engine. The regularization of the solution of a non-correct Volterra integral equation of the first kind for the initial distribution of temperatures by Laplace’s stochastic transformation in the square approximation reduces the first-kind equation to a second-kind equation, whose solution is unique and stable relative to the errors of initial data.

Keywords: heat conductivity, internal combustion engine, non-stationary operator
References: 

1. Lattes R., Lions Zh. Quasi-inversion method and its application, Moscow: Mir, 1970 (in Russian).
2. Lavrentiev M. M. Dokl. AN USSR, 1959, 127, Iss. 1: 12–15 (in Russian).
3. Krivoshey F. A. Dopov. Nac. akad. nauk Ukr., 1998, No 12: 108–112 (in Russian).
4. Lavrentiev M. M., Romanov V. G., Shyshatskiy S. P. Incorrect problems of mathematical physics, Moscow: Nauka, 1980 (in Russian).
5. Alifanov O. M., Artyukhin E. A, Rumyantsev S. V. Extreme methods for solving ill-posed problems and their applications to inverse problems of heat transfer, Moscow: Nauka, 1988 (in Russian).
6. Krivoshey F. A. Teoret. osnovy khim. tekhnologii, 1993, 33, No 7: 453–458 (in Russian).