Geodesic
Approximate analytic solution of heat conductivity problems with a~mismatch between initial and boundary conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 63-71.

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We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers ($0\le\mathsf F\infty$) and is especially effective for very small time intervals.
Keywords: approximate analytic solution, integral relation method, temperature disturbance front
Mots-clés : variable initial condition. 
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E. V. Stefanyuk; V. A. Kudinov. Approximate analytic solution of heat conductivity problems with a~mismatch between initial and boundary conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 63-71. http://geodesic.mathdoc.fr/item/IVM_2010_4_a6/

[1] Lykov A. V., Teoriya teploprovodnosti, Vysshaya shkola, M., 1967, 600 pp. | Zbl

[2] Gudmen T., “Primenenie integralnykh metodov v nelineinykh zadachakh nestatsionarnogo teploobmena”, Problemy teploobmena, Atomizdat, M., 1967, 41–96

[3] Belyaev N. M., Ryadno A. A., Metody nestatsionarnoi teploprovodnosti, Vysshaya shkola, M., 1978, 328 pp.

[4] Postolnik Yu. S., “Metod osredneniya funktsionalnykh popravok v zadachakh teploprovodnosti”, Teplo- i massoperenos, 8 (1972), 23–29

[5] Bio M., Variatsionnye printsipy v teorii teploobmena, Energiya, M., 1975, 209 pp. | Zbl

[6] Veinik A. I., Priblizhennyi raschet protsessov teploprovodnosti, Gosenergoizdat, M.–L., 1959, 184 pp.

[7] Kudinov V. A., Averin B. V., Stefanyuk E. V., “Resheniya zadach teploprovodnosti pri peremennykh vo vremeni granichnykh usloviyakh na osnove opredeleniya fronta temperaturnogo vozmuscheniya”, Izv. RAN. Ser. Energetika, 2007, no. 1, 55–68

[8] Kudinov V. A., Stefanyuk E. V., “Zadachi teploprovodnosti na osnove opredeleniya fronta temperaturnogo vozmuscheniya”, Izv. RAN. Ser. Energetika, 2008, no. 5, 141–157