Retrospective task for a non-stationary operator of heat conductivity

TitleRetrospective task for a non-stationary operator of heat conductivity
Publication TypeJournal Article
Year of Publication2014
AuthorsPanin, VV, Krivoshey, FA, Bogdan, Yu.A
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
SectionHeat Physics
Date Published8/2014

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.

Keywordsheat conductivity, internal combustion engine, non-stationary operator

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).