The 9 references with contexts in paper P. Vlasov A., П. Власов А. (2016) “Влияние равномерного движения границы на температурное поле полупространства, подверженного нагреву внешним тепловым потоком // The Influence of the Boundary Motion on Temperature Field in the Half-Space Under External Heat Flux” / spz:neicon:technomag:y:2014:i:8:p:101-109

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Kartashov E.M.Analiticheskie metody v teorii teploprovodnosti tverdykh tel[Analytic methods in the theory of thermal conductivity of solids]. Moscow, Vysshaia shkola Publ., 1985. 553 p. (in Russian).
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    ›ÚË Ô‰ÒÚ‡‚ÎÂÌˡ ÏÓ„ÛÚ · ̊Ú ̧ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ Ì ÚÓÎ ̧ÍÓ ‰Îˇ Ôӂ‰ÂÌˡ Ô‡‡ÏÂÚË ̃ÂÒÍÓ„Ó ‡Ì‡ÎËÁ‡ ÚÂÏÔÂ‡ÚÌÓ„Ó ÔÓΡ ËÁÛ ̃‡ÂÏÓÈ ÒËÒÚÂÏ ̊ Ò ˆÂÎ ̧ ̨ ÓÔÚËÏËÁ‡ˆËË Â ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊, ÌÓ Ë ‰Îˇ ÚÂÒÚËÓ‚‡Ìˡ ‚ÌÓ‚ ̧ ÒÓÁ‰‡‚‡ÂÏ ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ÍÓÏÔÎÂÍÒÓ‚. —ÎÓÊÌÓÒÚË, ‚ÓÁÌË͇ ̨ ̆Ë ÔË ÔÓËÒÍ ڇÍËı  ̄ÂÌËÈ, ıÓÓ ̄Ó ÓÔËÒ‡Ì ̊ ‚ ÎËÚÂ‡ÚÛÂ
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    . —ΉÛÂÚ Á‡ÏÂÚËÚ ̧, ̃ÚÓ ‚Ó ÏÌÓ„Ëı Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ı ËÌÊÂÌÂÌ ̊ı Á‡‰‡ ̃‡ı ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ËÁÛ ̃‡ÂÏÓÈ ÍÓÌÒÚÛ͈ËË ÒÓÔÓ‚Óʉ‡ÂÚÒˇ ÛÌÓÒÓÏ ̃‡ÒÚË ‚ ̆ÂÒÚ‚‡ Ò ÔÓ‚ÂıÌÓÒÚË, ̃ÚÓ ÔË‚Ó‰ËÚ Í ËÁÏÂÌÂÌË ̨  „‡Ìˈ ‚Ó ‚ÂÏÂÌË.

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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
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    . “‡Í, ‚ ‡·ÓÚ [6] Á‡‰‡ ̃‡ ̇ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ÔÓ‰‚ËÊÌÓÈ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ÌÂÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓÓ·ÏÂ̇ Ò ‚Ì ̄ÌÂÈ Ò‰ÓÈ Ò‚Â‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡. ÷ÂÎ ̧ ̨ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ ˇ‚ΡÂÚÒˇ ËÁÛ ̃ÂÌË ‚ÎˡÌˡ ‡‚ÌÓÏÂÌÓ„Ó ‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ, ̇ ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ Â„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ÛÒÎӂˡı ‚ÓÁ‰ÂÈÒڂˡ ÒÚ

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Kartashov E.M., Liubov B.Ia. Analytical methods for solving boundary value problems for the heat equation in a region with moving boundaries.Izv. AN SSSR. Energetika i transport= Proceedings of the USSR AS. Power engineering and transport, 1974, no. 6, pp. 83{111. (in Russian).
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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
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    . “‡Í, ‚ ‡·ÓÚ [6] Á‡‰‡ ̃‡ ̇ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ÔÓ‰‚ËÊÌÓÈ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ÌÂÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓÓ·ÏÂ̇ Ò ‚Ì ̄ÌÂÈ Ò‰ÓÈ Ò‚Â‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡. ÷ÂÎ ̧ ̨ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ ˇ‚ΡÂÚÒˇ ËÁÛ ̃ÂÌË ‚ÎˡÌˡ ‡‚ÌÓÏÂÌÓ„Ó ‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ, ̇ ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ Â„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ÛÒÎӂˡı ‚ÓÁ‰ÂÈÒڂˡ ÒÚ

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Kartashov E.M. Analytical Methods of Solution of Boundary | Value Problems of Nonstationary Heat Conduction in Regions with Moving Boundaries.Izv. RAN. Energetika=Proceedings of the RAS. Power engineering, 1999, no. 5, pp. 3{34. (in Russian).
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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
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    . “‡Í, ‚ ‡·ÓÚ [6] Á‡‰‡ ̃‡ ̇ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ÔÓ‰‚ËÊÌÓÈ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ÌÂÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓÓ·ÏÂ̇ Ò ‚Ì ̄ÌÂÈ Ò‰ÓÈ Ò‚Â‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡. ÷ÂÎ ̧ ̨ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ ˇ‚ΡÂÚÒˇ ËÁÛ ̃ÂÌË ‚ÎˡÌˡ ‡‚ÌÓÏÂÌÓ„Ó ‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ, ̇ ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ Â„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ÛÒÎӂˡı ‚ÓÁ‰ÂÈÒڂˡ ÒÚ

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Kartashov E.M. Analytical Methods of Solution of Boundary | Value Problems of Nonstationary Heat Conduction in Regions with Moving Boundaries.Inzhenerno-fizicheskii zhurnal, 2001, vol. 74, no. 2, pp. 171{195. (English translation:Journal of Engineering Physics and Thermophysics, 2001, vol. 74, iss. 2, pp. 498{536. DOI:10.1023/A:1016641613982).
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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
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    . “‡Í, ‚ ‡·ÓÚ [6] Á‡‰‡ ̃‡ ̇ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ÔÓ‰‚ËÊÌÓÈ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ÌÂÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓÓ·ÏÂ̇ Ò ‚Ì ̄ÌÂÈ Ò‰ÓÈ Ò‚Â‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡. ÷ÂÎ ̧ ̨ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ ˇ‚ΡÂÚÒˇ ËÁÛ ̃ÂÌË ‚ÎˡÌˡ ‡‚ÌÓÏÂÌÓ„Ó ‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ, ̇ ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ Â„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ÛÒÎӂˡı ‚ÓÁ‰ÂÈÒڂˡ ÒÚ

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Attetkov A.V., Vlasov P.A., Volkov I.K. Temperature Field of a Half-Space with a Thermally Thin Coating in Pulse Modes of Heat Exchange with the Environment.Inzhenerno-fizicheskii zhurnal, 2001, vol. 74, no. 3, pp. 81{86. (English translation:Journal of Engineering Physics and Thermophysics, 2001, vol. 74, iss. 3, pp. 647{655. DOI:10.1023/A:1016756227188).
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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
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Attetkov A.V., Vlasov P.A., Volkov I.K. Influence of the Mobility of a Boundary on the Temperature Field of a Half-Space under Unstable Conditions of Heat Exchange with the Environment.Inzhenerno-fizicheskii zhurnal, 2001, vol. 75, no. 6, pp. 172{178. (English translation: Journal of Engineering Physics and Thermophysics, 2001, vol. 75, iss. 6, pp. 1454{1462. DOI: 10.1023/A:1022143716313).
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    ÕÂÓ·ıÓ‰ËÏÓÒÚ ̧ Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏÓÈ Ó·Î‡ÒÚË ÒÛ ̆ÂÒÚ‚ÂÌÌÓ ÛÒÎÓÊÌˇÂÚ ÔÓÎÛ ̃ÂÌË ‡Ì‡ÎËÚË ̃ÂÒÍËı  ̄ÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃ ‰‡Ê ‚ ÔÓÒÚÂÈ ̄Ëı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ [1,2,3,4,5]. “‡Í, ‚ ‡·ÓÚÂ
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    Á‡‰‡ ̃‡ ̇ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ÔÓ‰‚ËÊÌÓÈ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ÌÂÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓÓ·ÏÂ̇ Ò ‚Ì ̄ÌÂÈ Ò‰ÓÈ Ò‚Â‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡. ÷ÂÎ ̧ ̨ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ ˇ‚ΡÂÚÒˇ ËÁÛ ̃ÂÌË ‚ÎˡÌˡ ‡‚ÌÓÏÂÌÓ„Ó ‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ, ̇ ÔÓˆÂÒÒ ÙÓÏËÓ‚‡Ìˡ Â„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ‚ ÛÒÎӂˡı ‚ÓÁ‰ÂÈÒڂˡ ÒÚ‡ˆËÓ̇ÌÓ„Ó ÚÂÔÎÓ‚Ó

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Volkov I.K., Kanatnikov A.N.Integral'nye preobrazovaniia i operatsionnoe ischislenie[Integral transforms and operational calculus]. Moscow, Bauman MSTU Publ., 1996. 288 p. (in Russian).
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    ÔË Í‡Ê‰ÓÏ ÙËÍÒËÓ‚‡ÌÌÓÏ Á̇ ̃ÂÌËËFo>0ÙÛÌÍˆËˇθ(ξ,Fo)ËÌÚ„ËÛÂχ Ò Í‚‡‰‡ÚÓÏ ÔÓ ÔÓÒÚ‡ÌÒÚ‚ÂÌÌÓÈ ÔÂÂÏÂÌÌÓÈξ∈[V0Fo,+∞). ÓÏ ÚÓ„Ó, ·Û‰ÂÏ Ô‰ÔÓ·„‡Ú ̧, ̃ÚÓ ‰Îˇ Í‡Ê‰Ó„Ó Á̇ ̃ÂÌˡξÙÛÌÍˆËˇθ(ξ,·)ˇ‚ΡÂÚÒˇ ÓË„Ë̇ÎÓÏ ÔÂÓ·‡ÁÓ‚‡Ìˡ À‡Ô·҇
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    . ƒÎˇ  ̄ÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓÈ Á‡‰‡ ̃Ë Û‰Ó·ÌÓ Ò‰ÂÎ‡Ú ̧ Á‡ÏÂÌÛ ÔÂÂÏÂÌÌ ̊ı x=ξ−V0Fo, τ= Fo, ÔÂÂȉˇ ‚ ÒËÒÚÂÏÛ ÍÓÓ‰Ë̇Ú, Ò‚ˇÁ‡ÌÌÛ ̨ Ò ‰‚ËÊÛ ̆ÂÈÒˇ „‡ÌˈÂÈ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡. ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ÏÓ‰ÂÎ ̧ (1){(3) ÔËÏÂÚ ÒÎÂ‰Û ̨ ̆ËÈ ‚ˉ: ∂θ(x, τ) ∂τ = ∂2θ(x, τ) ∂x2 +V0 ∂θ(x, τ) ∂x , x >0, τ >0,(5) θ(x,0) = 0, x >0,(6) ∂θ(x, τ) ∂x ∣ ∣ ∣ ∣ x=0 =−Q, τ>0,(7) ‡ ÛÒÎÓ‚Ë (4) Á‡ÔË ̄ÂÚÒˇ ‚ ‚ˉ θ(x, τ) ∣ ∣

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    “‡ÍËÏ Ó·‡ÁÓÏ,  ̄ÂÌË Á‡‰‡ ̃Ë (9)|(11) ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ ‚ˉ u(x, s) = Q s(V1+ √ V21+s) e−x(V1+ √ V21+s).(13) ÕÂÔÓÒ‰ÒÚ‚ÂÌÌ ̊È ÔÂÂıÓ‰ ÓÚ ËÁÓ·‡ÊÂÌˡu(x, s), ÓÔ‰ÂΡÂÏÓ„Ó ‡‚ÂÌÒÚ‚ÓÏ (13), Í ÓË„Ë̇ÎÛθ(x, τ)Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ Ú‡·Îˈ <ËÁÓ·‡ÊÂÌË | ÓË„Ë̇Î> ‚ÓÁÏÓÊÂÌ [8], ÌÓ ÌÂ Ó ̃ÂÌ ̧ Û‰Ó·ÂÌ. œÓ ̋ÚÓÏÛ ‰Îˇ ̇ıÓʉÂÌˡ  ̄ÂÌˡ Á‡‰‡ ̃Ë (5)|(8) ‚ÓÒÔÓÎ ̧ÁÛÂÏÒˇ ÙÓÏÛÎÓÈ Ó·‡ ̆ÂÌˡ
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    θ(x, τ) = 1 2πi σ+i∞∫ σ−i∞ esτu(x, s)ds.(14) ‘ÛÌÍˆËˇu(x, s)ËÏÂÂÚ ‰‚ ÓÒÓ· ̊ ÚÓ ̃ÍËs= 0Ës=−V21=−V20/4, ÍÓÚÓ ̊ ˇ‚Ρ ̨ÚÒˇ ÔÓÒÚ ̊Ï ÔÓÎ ̨ÒÓÏ Ë ÚÓ ̃ÍÓÈ ‚ÂÚ‚ÎÂÌˡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ, ÔÓ ̋ÚÓÏÛ ‡ÒÒÏÓÚËÏ Ô‰ÒÚ‡‚ÎÂÌÌ ̊È Ì‡ ËÒ.1ÍÓÌÚÛK, „‰Â x A1A2, x A5A6Ë x A3A4, | ‰Û„Ë ÓÍÛÊÌÓÒÚÂÈ ‡‰ËÛÒÓ‚RËρÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Ò ˆÂÌÚ‡ÏË ‚ ÚÓ ̃ÍÂ−V21=−V20/4. œÓÒÍÓÎ ̧ÍÛ Ó·ıÓ‰ ÍÓÌÚÛ‡ ÒÓ‚Â ̄‡ÂÚÒˇ ÔÓÚË‚ ̃‡ÒÓ‚ÓÈ ÒÚÂÎÍË, ÚÓ

8
Lykov A.V.Teoriia teploprovodnosti[Theory of Heat Conduction]. Moscow, Vysshaia shkola Publ., 1967. 600 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=5090
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    “‡ÍËÏ Ó·‡ÁÓÏ,  ̄ÂÌË Á‡‰‡ ̃Ë (9)|(11) ÏÓÊÌÓ Ô‰ÒÚ‡‚ËÚ ̧ ‚ ‚ˉ u(x, s) = Q s(V1+ √ V21+s) e−x(V1+ √ V21+s).(13) ÕÂÔÓÒ‰ÒÚ‚ÂÌÌ ̊È ÔÂÂıÓ‰ ÓÚ ËÁÓ·‡ÊÂÌˡu(x, s), ÓÔ‰ÂΡÂÏÓ„Ó ‡‚ÂÌÒÚ‚ÓÏ (13), Í ÓË„Ë̇ÎÛθ(x, τ)Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ Ú‡·Îˈ <ËÁÓ·‡ÊÂÌË | ÓË„Ë̇Î> ‚ÓÁÏÓÊÂÌ
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    , ÌÓ ÌÂ Ó ̃ÂÌ ̧ Û‰Ó·ÂÌ. œÓ ̋ÚÓÏÛ ‰Îˇ ̇ıÓʉÂÌˡ  ̄ÂÌˡ Á‡‰‡ ̃Ë (5)|(8) ‚ÓÒÔÓÎ ̧ÁÛÂÏÒˇ ÙÓÏÛÎÓÈ Ó·‡ ̆ÂÌˡ [7] θ(x, τ) = 1 2πi σ+i∞∫ σ−i∞ esτu(x, s)ds.(14) ‘ÛÌÍˆËˇu(x, s)ËÏÂÂÚ ‰‚ ÓÒÓ· ̊ ÚÓ ̃ÍËs= 0Ës=−V21=−V20/4, ÍÓÚÓ ̊ ˇ‚Ρ ̨ÚÒˇ ÔÓÒÚ ̊Ï ÔÓÎ ̨ÒÓÏ Ë ÚÓ ̃ÍÓÈ ‚ÂÚ‚ÎÂÌˡ ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ, ÔÓ ̋ÚÓÏÛ ‡ÒÒÏÓÚËÏ Ô‰ÒÚ‡‚ÎÂÌÌ ̊È Ì‡ ËÒ.1ÍÓÌÚÛK, „‰Â x A1A2, x A5A6Ë x A3A4, | ‰Û„Ë ÓÍÛÊÌÓÒÚÂÈ ‡‰ËÛÒÓ‚RËρÒ

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Ditkin V.A., Prudnikov A.V.Spravochnik po operatsionnomu ischisleniiu[Handbook of Operational Calculus]. Moscow, Vysshaia shkola Publ., 1965. 468 p. (in Russian).
Total in-text references: 1
  1. In-text reference with the coordinate start=6142
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    ÃÓÊÌÓ ÔÓ͇Á‡Ú ̧, ̃ÚÓ ÒÛ ̆ÂÒÚ‚Û ̨ÚM0>0ËR0>0, Ú‡ÍËÂ, ̃ÚÓ ‰Îˇ ‚ÒÂıR>R0,x>0ÙÛÌÍˆËˇu(x, s) ÔËs, ÔË̇‰ÎÂʇ ̆ÂÏ ÓÍÛÊÌÓÒÚË{z∈C:|z+V21|=R}, Û‰Ó‚ÎÂÚ‚ÓˇÂÚ ÌÂ‡‚ÂÌÒÚ‚Û |u(x, s)|6 M0 R2 . ¬ ÒÓÓÚ‚ÂÚÒÚ‚ËË Ò ÎÂÏÏÓÈ ∆Ó‰‡Ì‡
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    ËÁ ̋ÚÓ„Ó ÒΉÛÂÚ, ̃ÚÓ I1= 1 2πi lim R→+∞ ∫ x A1A2∪ x A5A6 esτu(x, s)ds= 0.(16) ≈ÒÎËs∈ x A3A4, ÚÓs=ρeiφ−V21,ds=ρieiφdφ, Ë, Òӄ·ÒÌÓ (13), I2= 1 2πi lim ρ→0+ ∫ x A3A4 esτu(x, s)ds= = Qe−xV1 2πi ∫ −ππ ( lim ρ→0+ eρτexpiφe−x √ρexpiφ/2 (ρeiφ−V21) √ ρeiφ/2 ρieiφ ) dφ= 0.(17) ƒÎˇ ‚ ̊ ̃ËÒÎÂÌˡ ËÌÚ„‡Î‡ I3= 1 2πi lim R→+∞ ρ→0+ ∫ → A2A3∪ → A4A5 esτu(x, s)ds(18) ‚‰ÓÎ ̧ ‡ÁÂÁ‡ → A2A3∪ → A4A5҉·ÂÏ Ô‰‚