The 20 reference contexts in paper P. Vlasov A., П. Власов А. (2016) “Исследование влияния подвижности границы на температурное поле полупространства при воздействии теплового потока // Research of the Border Mobility Influence on the Half-Space Temperature Field Under Heat Flux” / spz:neicon:technomag:y:2014:i:0:p:137-151

  1. Start
    1582
    Prefix
    ¬Ó ÏÌÓ„ÓÏ ̋ÚÓ Ó· ̇ˇÒÌˇÂÚÒˇ ÚÂÏ, ̃ÚÓ ÔÓÎÛ ̃ÂÌÌ ̊Â Ò Ëı ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ Ô‰ÒÚ‡‚ÎÂÌˡ  ̄ÂÌËÈ ÏÓ„ÛÚ · ̊Ú ̧ ËÒÔÓÎ ̧ÁÓ‚‡Ì ̊ Í‡Í ‰Îˇ Ô‡‡ÏÂÚË ̃ÂÒÍÓÈ ‡Ì‡ÎËÁ‡ ÚÂÔÎÓ‚Ó„Ó ÒÓÒÚÓˇÌˡ ËÁÛ ̃‡ÂÏÓÈ ÒËÒÚÂÏ ̊, Ú‡Í Ë ‰Îˇ ÚÂÒÚËÓ‚‡Ìˡ ‡Á‡·‡Ú ̊‚‡ÂÏ ̊ı ‚ ̊ ̃ËÒÎËÚÂÎ ̧Ì ̊ı ‡Î„ÓËÚÏÓ‚. “Û‰ÌÓÒÚË, ‚ÓÁÌË͇ ̨ ̆Ë ÔË ÔÓÎÛ ̃ÂÌËË ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ  ̄ÂÌËÈ Á‡‰‡ ̃ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË, ıÓÓ ̄Ó ËÁ‚ÂÒÚÌ ̊
    Exact
    [1]
    Suffix
    . ÃÌÓ„Ë Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ ËÌÊÂÌÂÌ ̊ Á‡‰‡ ̃Ë, Ò‚ˇÁ‡ÌÌ ̊Â Ò ‡Ò ̃ÂÚÓÏ Ë ÓÔÚËÏËÁ‡ˆËÂÈ ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊ ‡ ̋ÓÍÓÒÏË ̃ÂÒÍËı ÒËÒÚÂÏ, ÚÂ·Û ̨Ú Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏ ̊ı ÍÓÌÒÚÛ͈ËÈ [2]. œË ̋ÚÓÏ ÒÎÓÊÌÓÒÚË, Ò‚ˇÁ‡ÌÌ ̊Â Ò ÔÓÎÛ ̃ÂÌËÂÏ ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃, Á̇ ̃ËÏÓ ‚ÓÁ‡ÒÚ‡ ̨Ú ‰‡Ê ‚ ÚÂı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ [1]|[6].
    (check this in PDF content)

  2. Start
    1774
    Prefix
    “Û‰ÌÓÒÚË, ‚ÓÁÌË͇ ̨ ̆Ë ÔË ÔÓÎÛ ̃ÂÌËË ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ  ̄ÂÌËÈ Á‡‰‡ ̃ ÚÂÔÎÓÔÓ‚Ó‰ÌÓÒÚË, ıÓÓ ̄Ó ËÁ‚ÂÒÚÌ ̊ [1]. ÃÌÓ„Ë Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ ËÌÊÂÌÂÌ ̊ Á‡‰‡ ̃Ë, Ò‚ˇÁ‡ÌÌ ̊Â Ò ‡Ò ̃ÂÚÓÏ Ë ÓÔÚËÏËÁ‡ˆËÂÈ ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊ ‡ ̋ÓÍÓÒÏË ̃ÂÒÍËı ÒËÒÚÂÏ, ÚÂ·Û ̨Ú Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏ ̊ı ÍÓÌÒÚÛ͈ËÈ
    Exact
    [2]
    Suffix
    . œË ̋ÚÓÏ ÒÎÓÊÌÓÒÚË, Ò‚ˇÁ‡ÌÌ ̊Â Ò ÔÓÎÛ ̃ÂÌËÂÏ ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃, Á̇ ̃ËÏÓ ‚ÓÁ‡ÒÚ‡ ̨Ú ‰‡Ê ‚ ÚÂı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ [1]|[6]. “‡Í, ‚ ‡·ÓÚ [7] Á‡‰‡ ̃‡ ÓÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌÂÈ Ò‰ÓÈ, ҂‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ, ̃ÚÓ ÔÓÁ‚ÓÎËÎÓ ËÁÛ ̃ËÚ ̧
    (check this in PDF content)

  3. Start
    1961
    Prefix
    ÃÌÓ„Ë Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ ËÌÊÂÌÂÌ ̊ Á‡‰‡ ̃Ë, Ò‚ˇÁ‡ÌÌ ̊Â Ò ‡Ò ̃ÂÚÓÏ Ë ÓÔÚËÏËÁ‡ˆËÂÈ ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊ ‡ ̋ÓÍÓÒÏË ̃ÂÒÍËı ÒËÒÚÂÏ, ÚÂ·Û ̨Ú Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏ ̊ı ÍÓÌÒÚÛ͈ËÈ [2]. œË ̋ÚÓÏ ÒÎÓÊÌÓÒÚË, Ò‚ˇÁ‡ÌÌ ̊Â Ò ÔÓÎÛ ̃ÂÌËÂÏ ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃, Á̇ ̃ËÏÓ ‚ÓÁ‡ÒÚ‡ ̨Ú ‰‡Ê ‚ ÚÂı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ
    Exact
    [1]
    Suffix
    |[6]. “‡Í, ‚ ‡·ÓÚ [7] Á‡‰‡ ̃‡ ÓÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌÂÈ Ò‰ÓÈ, ҂‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ, ̃ÚÓ ÔÓÁ‚ÓÎËÎÓ ËÁÛ ̃ËÚ ̧ ı‡‡ÍÚÂÌ ̊ ÓÒÓ·ÂÌÌÓÒÚË ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ËÁÛ ̃‡ÂÏÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ.
    (check this in PDF content)

  4. Start
    1965
    Prefix
    ÃÌÓ„Ë Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ ËÌÊÂÌÂÌ ̊ Á‡‰‡ ̃Ë, Ò‚ˇÁ‡ÌÌ ̊Â Ò ‡Ò ̃ÂÚÓÏ Ë ÓÔÚËÏËÁ‡ˆËÂÈ ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊ ‡ ̋ÓÍÓÒÏË ̃ÂÒÍËı ÒËÒÚÂÏ, ÚÂ·Û ̨Ú Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏ ̊ı ÍÓÌÒÚÛ͈ËÈ [2]. œË ̋ÚÓÏ ÒÎÓÊÌÓÒÚË, Ò‚ˇÁ‡ÌÌ ̊Â Ò ÔÓÎÛ ̃ÂÌËÂÏ ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃, Á̇ ̃ËÏÓ ‚ÓÁ‡ÒÚ‡ ̨Ú ‰‡Ê ‚ ÚÂı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ [1]|
    Exact
    [6]
    Suffix
    . “‡Í, ‚ ‡·ÓÚ [7] Á‡‰‡ ̃‡ ÓÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌÂÈ Ò‰ÓÈ, ҂‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ, ̃ÚÓ ÔÓÁ‚ÓÎËÎÓ ËÁÛ ̃ËÚ ̧ ı‡‡ÍÚÂÌ ̊ ÓÒÓ·ÂÌÌÓÒÚË ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ËÁÛ ̃‡ÂÏÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ.
    (check this in PDF content)

  5. Start
    1984
    Prefix
    „Ë Ô‡ÍÚË ̃ÂÒÍË ‚‡ÊÌ ̊ ËÌÊÂÌÂÌ ̊ Á‡‰‡ ̃Ë, Ò‚ˇÁ‡ÌÌ ̊Â Ò ‡Ò ̃ÂÚÓÏ Ë ÓÔÚËÏËÁ‡ˆËÂÈ ÚÂÔÎÓ‚ÓÈ Á‡ ̆ËÚ ̊ ‡ ̋ÓÍÓÒÏË ̃ÂÒÍËı ÒËÒÚÂÏ, ÚÂ·Û ̨Ú Û ̃ÂÚ‡ ÔÓ‰‚ËÊÌÓÒÚË „‡Ìˈ ËÁÛ ̃‡ÂÏ ̊ı ÍÓÌÒÚÛ͈ËÈ [2]. œË ̋ÚÓÏ ÒÎÓÊÌÓÒÚË, Ò‚ˇÁ‡ÌÌ ̊Â Ò ÔÓÎÛ ̃ÂÌËÂÏ ‡Ì‡ÎËÚË ̃ÂÒÍËı Ô‰ÒÚ‡‚ÎÂÌËÈ ÒÓÓÚ‚ÂÚÒÚ‚Û ̨ ̆Ëı Á‡‰‡ ̃, Á̇ ̃ËÏÓ ‚ÓÁ‡ÒÚ‡ ̨Ú ‰‡Ê ‚ ÚÂı ÒÎÛ ̃‡ˇı, ÍÓ„‰‡ Á‡ÍÓÌ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ËÁ‚ÂÒÚÂÌ [1]|[6]. “‡Í, ‚ ‡·ÓÚÂ
    Exact
    [7]
    Suffix
    Á‡‰‡ ̃‡ ÓÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌÂÈ Ò‰ÓÈ, ҂‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ, ̃ÚÓ ÔÓÁ‚ÓÎËÎÓ ËÁÛ ̃ËÚ ̧ ı‡‡ÍÚÂÌ ̊ ÓÒÓ·ÂÌÌÓÒÚË ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ËÁÛ ̃‡ÂÏÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ.
    (check this in PDF content)

  6. Start
    2310
    Prefix
    “‡Í, ‚ ‡·ÓÚ [7] Á‡‰‡ ̃‡ ÓÔ‰ÂÎÂÌˡ ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌÂÈ Ò‰ÓÈ, ҂‰Â̇ Í Á‡‰‡ ̃  ̄ÂÌˡ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ, ̃ÚÓ ÔÓÁ‚ÓÎËÎÓ ËÁÛ ̃ËÚ ̧ ı‡‡ÍÚÂÌ ̊ ÓÒÓ·ÂÌÌÓÒÚË ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ËÁÛ ̃‡ÂÏÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ. ¬ ‡·ÓÚÂ
    Exact
    [8]
    Suffix
    ÔÓÎÛ ̃ÂÌÓ ‡Ì‡ÎËÚË ̃ÂÒÍÓ Ô‰ÒÚ‡‚ÎÂÌË  ̄ÂÌˡ Á‡‰‡ ̃Ë Ì‡ıÓʉÂÌˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ Ò ‡‚ÌÓÏÂÌÓ ‰‚ËÊÛ ̆ÂÈÒˇ „‡ÌˈÂÈ, ÔÓ‰‚ÂÊÂÌÌÓ„Ó Ì‡„Â‚Û ‚Ì ̄ÌËÏ ÚÂÔÎÓ‚ ̊Ï ÔÓÚÓÍÓÏ. ŒÒÌӂ̇ˇ ˆÂÎ ̧ ̇ÒÚÓˇ ̆ÂÈ ‡·ÓÚ ̊ | ËÁÛ ̃ÂÌË ÓÒÓ·ÂÌÌÓÒÚÂÈ ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡ Ú‚Â‰Ó„Ó Ú·, ÏÓ‰ÂÎËÛÂÏÓ„Ó ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚ÓÏ Ò ‰‚ËÊÛ ̆ÂÈÒˇ ÔÓ ËÁ‚ÂÒÚÌÓÏÛ Á‡ÍÓÌÛl=l(Fo)„‡ÌˈÂÈ, ‚ ÛÒÎӂˡı
    (check this in PDF content)

  7. Start
    3940
    Prefix
    ÔË Í‡Ê‰ÓÏ ÙËÍÒËÓ‚‡ÌÌÓÏ Á̇ ̃ÂÌËË Fo>0ÙÛÌÍˆËˇθ(ξ,Fo)ËÌÚ„ËÛÂχ Ò Í‚‡‰‡ÚÓÏ ÔÓ ÔÓÒÚ‡ÌÒÚ‚ÂÌÌÓÈ ÔÂÂÏÂÌÌÓÈξ∈[l(Fo),+∞). ÓÏ ÚÓ„Ó, ·Û‰ÂÏ Ô‰ÔÓ·„‡Ú ̧, ̃ÚÓ ‰Îˇ Í‡Ê‰Ó„Ó Á̇ ̃ÂÌˡ Fo ÙÛÌÍˆËˇθ(·,Fo)ˇ‚ΡÂÚÒˇ ÓË„Ë̇ÎÓÏ ÔÂÓ·‡ÁÓ‚‡Ìˡ ‘Û ̧Â
    Exact
    [11]
    Suffix
    . ŒÚÌÓÒËÚÂÎ ̧ÌÓ Á‡ÍÓ̇ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ·Û‰ÂÏ Ô‰ÔÓ·„‡Ú ̧, ̃ÚÓl=l(Fo)| ÌÂÛ· ̊‚‡ ̨ ̆‡ˇ ÌÂÓÚˈ‡ÚÂÎ ̧̇ˇ ÙÛÌÍˆËˇ, ‰ËÙÙÂÂ̈ËÛÂχˇ ıÓÚˇ · ̊ ‚ Ó·Ó· ̆ÂÌÌÓÏ ÒÏ ̊ÒÎÂ,l(0) = 0, ‡Q=Q(Fo)Û‰Ó‚ÎÂÚ‚ÓˇÂÚ Òڇ̉‡ÚÌ ̊Ï Ú·ӂ‡ÌËˇÏ ÚÂÓÂÏ ̊ ÒÛ ̆ÂÒÚ‚Ó‚‡Ìˡ Ë Â‰ËÌÒÚ‚ÂÌÌÓÒÚË  ̄ÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓÈ Á‡‰‡ ̃Ë [9]. ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ÏÓÊÌÓ ‚ ̊ÔÓÎÌËÚ ̧ Á‡ÏÂÌÛ ÔÂÂÏÂÌÌ ̊ı x=ξ−l(Fo), τ=Fo,(5) ÔÓÒΠ̃Â„Ó Ï‡ÚÂχÚË ̃ÂÒÍ
    (check this in PDF content)

  8. Start
    4239
    Prefix
    ŒÚÌÓÒËÚÂÎ ̧ÌÓ Á‡ÍÓ̇ ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ·Û‰ÂÏ Ô‰ÔÓ·„‡Ú ̧, ̃ÚÓl=l(Fo)| ÌÂÛ· ̊‚‡ ̨ ̆‡ˇ ÌÂÓÚˈ‡ÚÂÎ ̧̇ˇ ÙÛÌÍˆËˇ, ‰ËÙÙÂÂ̈ËÛÂχˇ ıÓÚˇ · ̊ ‚ Ó·Ó· ̆ÂÌÌÓÏ ÒÏ ̊ÒÎÂ,l(0) = 0, ‡Q=Q(Fo)Û‰Ó‚ÎÂÚ‚ÓˇÂÚ Òڇ̉‡ÚÌ ̊Ï Ú·ӂ‡ÌËˇÏ ÚÂÓÂÏ ̊ ÒÛ ̆ÂÒÚ‚Ó‚‡Ìˡ Ë Â‰ËÌÒÚ‚ÂÌÌÓÒÚË  ̄ÂÌˡ ‡ÒÒχÚË‚‡ÂÏÓÈ Á‡‰‡ ̃Ë
    Exact
    [9]
    Suffix
    . ¬ ̋ÚÓÏ ÒÎÛ ̃‡Â ÏÓÊÌÓ ‚ ̊ÔÓÎÌËÚ ̧ Á‡ÏÂÌÛ ÔÂÂÏÂÌÌ ̊ı x=ξ−l(Fo), τ=Fo,(5) ÔÓÒΠ̃Â„Ó Ï‡ÚÂχÚË ̃ÂÒ͇ˇ ÏÓ‰ÂÎ ̧ (1){(3) ÔËÏÂÚ ÒÎÂ‰Û ̨ ̆ËÈ ‚ˉ: ∂θ(x, τ) ∂τ = ∂2θ(x, τ) ∂x2 +l′(τ) ∂θ(x, τ) ∂x , x >0, τ >0,(6) θ(x,0) = 0, x >0,(7) ∂θ(x, τ) ∂x ∣ ∣ ∣ ∣ ∣ x=0 =−Q(τ), τ >0,(8) ‡ ÛÒÎÓ‚Ë (4) Á‡ÔË ̄ÂÚÒˇ ‚ ‚ˉ θ(x, τ) ∣ ∣ ∣ ∣ τ >0 ∈L2[0,+∞).(9) 2.
    (check this in PDF content)

  9. Start
    4721
    Prefix
    τ=Fo,(5) ÔÓÒΠ̃Â„Ó Ï‡ÚÂχÚË ̃ÂÒ͇ˇ ÏÓ‰ÂÎ ̧ (1){(3) ÔËÏÂÚ ÒÎÂ‰Û ̨ ̆ËÈ ‚ˉ: ∂θ(x, τ) ∂τ = ∂2θ(x, τ) ∂x2 +l′(τ) ∂θ(x, τ) ∂x , x >0, τ >0,(6) θ(x,0) = 0, x >0,(7) ∂θ(x, τ) ∂x ∣ ∣ ∣ ∣ ∣ x=0 =−Q(τ), τ >0,(8) ‡ ÛÒÎÓ‚Ë (4) Á‡ÔË ̄ÂÚÒˇ ‚ ‚ˉ θ(x, τ) ∣ ∣ ∣ ∣ τ >0 ∈L2[0,+∞).(9) 2. – ̄ÂÌË ÔÓÒÚ‡‚ÎÂÌÌÓÈ Á‡‰‡ ̃Ë ƒÎˇ  ̄ÂÌˡ Á‡‰‡ ̃Ë (6){(8) ‚ÓÒÔÓÎ ̧ÁÛÂÏÒˇ ÍÓÒËÌÛÒ- Ë ÒËÌÛÒ- ÔÂÓ·‡ÁÓ‚‡ÌˡÏË ‘Û ̧Â
    Exact
    [10,11]
    Suffix
    ÔÓ ÔÓÒÚ‡ÌÒÚ‚ÂÌÌÓÈ ÔÂÂÏÂÌÌÓÈx. œËÏÂÌË‚ ÓÔÂ‡ÚÓ ÍÓÒËÌÛÒ-ÔÂÓ·‡ÁÓ‚‡Ìˡ Í Û‡‚ÌÂÌË ̨ (6) Ë Ì‡ ̃‡Î ̧ÌÓÏÛ ÛÒÎÓ‚Ë ̨ (7), Ò Û ̃ÂÚÓÏ (9) Ë „‡ÌË ̃ÌÓ„Ó ÛÒÎӂˡ (8) ÔËıÓ‰ËÏ Í ÒÎÂ‰Û ̨ ̆ÂÈ Á‡‰‡ ̃Â:    dΘC(p, τ) dτ =−p2ΘC(p, τ) +pl′(τ) ΘS(p, τ) +Q(τ)−l′(τ)θ(0, τ), τ >0; ΘC(p,0) = 0, (10) „‰ÂΘC(p, τ)| ËÁÓ·‡ÊÂÌË ÍÓÒËÌÛÒ-ÔÂÓ·‡ÁÓ‚‡Ìˡ ‘Û ̧ ÌÂËÁ‚ÂÒÚÌÓ„Ó  ̄ÂÌˡθ(ξ, τ), ‡p| Ô‡‡ÏÂÚ ̋ÚÓ„Ó ÔÂÓ·
    (check this in PDF content)

  10. Start
    6257
    Prefix
    ‚ÂÒÚÌÓ„Ó ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓΡθ(x, τ)ÔÓÎÌÓÒÚ ̧ ̨ ÓÔ‰ÂΡ ̨ÚÒˇ Â„Ó Á̇ ̃ÂÌˡÏËθ(0, τ)̇ „‡Ìˈ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡x>0, ÒÍÓÓÒÚ ̧ ̨l′(τ)‰‚ËÊÂÌˡ „‡Ìˈ ̊ Ë ÙÛÌ͈ËÂÈQ(τ), ÔËÌËχ ̨ ̆ÂÈ Á̇ ̃ÂÌˡ, ÔÓÔÓˆËÓ̇Π̧Ì ̊ Á̇ ̃ÂÌËˇÏ ‚Ì ̄ÌÂ„Ó ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇. ƒÎˇ  ̄ÂÌˡ Á‡‰‡ ̃Ë Ó ̄Ë (12) Á‡ÏÂÚËÏ, ̃ÚÓ ÂÒÎËR(τ, η)| ÂÁÓÎ ̧‚ÂÌÚ‡ ̋ÚÓÈ Á‡‰‡ ̃Ë, ÚÓ Â  ̄ÂÌË ÏÓÊÂÚ · ̊Ú ̧ Ô‰ÒÚ‡‚ÎÂÌÓ ‚ Òڇ̉‡ÚÌÓÈ ÙÓÏÂ
    Exact
    [12]
    Suffix
    : Θ(p, τ) = ∫τ 0 R(τ, η) [ f(η) +F(p, η)θ(0, η) ] dη.(15) œÓÒÍÓÎ ̧ÍÛ Òӄ·ÒÌÓ (13), (14) χÚË ̃Ì ̊ ÙÛÌ͈ËËA(p, τ)Ë ∫τ η A(p, χ)dχ=   −p2(τ−η)p[l(τ)−l(η)] −p[l(τ)−l(η)]−p2(τ−η)  ,06η6τ, ÍÓÏÏÛÚËÛ ̨Ú, ‚ ̃ÂÏ ÏÓÊÌÓ Û·Â‰ËÚ ̧Òˇ ÌÂÔÓÒ‰ÒÚ‚ÂÌÌÓÈ ÔÓ‚ÂÍÓÈ, ÚÓ [12] R(τ, η) = exp   ∫τ η A(p, χ)dχ  .(16) —ӄ·ÒÌÓ ÚÂÓÂÏ ̋ÎË | √‡ÏËÎ ̧ÚÓ̇ [12], ‰Îˇ Î ̨·ÓÈ Í‚‡‰‡ÚÌÓÈ Ï‡Úˈ ̊UÔÓˇ‰Í‡n  ı‡‡ÍÚÂ
    (check this in PDF content)

  11. Start
    6502
    Prefix
    Á‡‰‡ ̃Ë Ó ̄Ë (12) Á‡ÏÂÚËÏ, ̃ÚÓ ÂÒÎËR(τ, η)| ÂÁÓÎ ̧‚ÂÌÚ‡ ̋ÚÓÈ Á‡‰‡ ̃Ë, ÚÓ Â  ̄ÂÌË ÏÓÊÂÚ · ̊Ú ̧ Ô‰ÒÚ‡‚ÎÂÌÓ ‚ Òڇ̉‡ÚÌÓÈ ÙÓÏ [12]: Θ(p, τ) = ∫τ 0 R(τ, η) [ f(η) +F(p, η)θ(0, η) ] dη.(15) œÓÒÍÓÎ ̧ÍÛ Òӄ·ÒÌÓ (13), (14) χÚË ̃Ì ̊ ÙÛÌ͈ËËA(p, τ)Ë ∫τ η A(p, χ)dχ=   −p2(τ−η)p[l(τ)−l(η)] −p[l(τ)−l(η)]−p2(τ−η)  ,06η6τ, ÍÓÏÏÛÚËÛ ̨Ú, ‚ ̃ÂÏ ÏÓÊÌÓ Û·Â‰ËÚ ̧Òˇ ÌÂÔÓÒ‰ÒÚ‚ÂÌÌÓÈ ÔÓ‚ÂÍÓÈ, ÚÓ
    Exact
    [12]
    Suffix
    R(τ, η) = exp   ∫τ η A(p, χ)dχ  .(16) —ӄ·ÒÌÓ ÚÂÓÂÏ ̋ÎË | √‡ÏËÎ ̧ÚÓ̇ [12], ‰Îˇ Î ̨·ÓÈ Í‚‡‰‡ÚÌÓÈ Ï‡Úˈ ̊UÔÓˇ‰Í‡n  ı‡‡ÍÚÂËÒÚË ̃ÂÒÍËÈ ÏÌÓ„Ó ̃ÎÂÌq(λ)ˇ‚ΡÂÚÒˇ Ú‡Íʠ ‡ÌÌÛÎËÛ ̨ ̆ËÏ ÏÌÓ„Ó ̃ÎÂÌÓÏ, Ú.
    (check this in PDF content)

  12. Start
    6577
    Prefix
    ÏÓÊÂÚ · ̊Ú ̧ Ô‰ÒÚ‡‚ÎÂÌÓ ‚ Òڇ̉‡ÚÌÓÈ ÙÓÏ [12]: Θ(p, τ) = ∫τ 0 R(τ, η) [ f(η) +F(p, η)θ(0, η) ] dη.(15) œÓÒÍÓÎ ̧ÍÛ Òӄ·ÒÌÓ (13), (14) χÚË ̃Ì ̊ ÙÛÌ͈ËËA(p, τ)Ë ∫τ η A(p, χ)dχ=   −p2(τ−η)p[l(τ)−l(η)] −p[l(τ)−l(η)]−p2(τ−η)  ,06η6τ, ÍÓÏÏÛÚËÛ ̨Ú, ‚ ̃ÂÏ ÏÓÊÌÓ Û·Â‰ËÚ ̧Òˇ ÌÂÔÓÒ‰ÒÚ‚ÂÌÌÓÈ ÔÓ‚ÂÍÓÈ, ÚÓ [12] R(τ, η) = exp   ∫τ η A(p, χ)dχ  .(16) —ӄ·ÒÌÓ ÚÂÓÂÏ ̋ÎË | √‡ÏËÎ ̧ÚÓ̇
    Exact
    [12]
    Suffix
    , ‰Îˇ Î ̨·ÓÈ Í‚‡‰‡ÚÌÓÈ Ï‡Úˈ ̊UÔÓˇ‰Í‡n  ı‡‡ÍÚÂËÒÚË ̃ÂÒÍËÈ ÏÌÓ„Ó ̃ÎÂÌq(λ)ˇ‚ΡÂÚÒˇ Ú‡Íʠ ‡ÌÌÛÎËÛ ̨ ̆ËÏ ÏÌÓ„Ó ̃ÎÂÌÓÏ, Ú.Â., ÂÒÎË q(λ) = det(U−λEn)≡ ∑n k=0 qkλk, q(U) = ∑n k=0 qkUk=On, „‰Âqk,k=0, n, | ÍÓ ̋ÙÙˈËÂÌÚ ̊ ı‡‡ÍÚÂËÒÚË ̃ÂÒÍÓ„Ó ÏÌÓ„Ó ̃ÎÂ̇,U0=En,On| ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Â‰ËÌË ̃̇ˇ Ë Í‚‡‰‡Ú̇ˇ ÌÛ΂‡ˇ χÚˈ ̊ ÔÓˇ‰Í‡n.
    (check this in PDF content)

  13. Start
    7070
    Prefix
    Û ̨ ̆ËÏ ÏÌÓ„Ó ̃ÎÂÌÓÏ, Ú.Â., ÂÒÎË q(λ) = det(U−λEn)≡ ∑n k=0 qkλk, q(U) = ∑n k=0 qkUk=On, „‰Âqk,k=0, n, | ÍÓ ̋ÙÙˈËÂÌÚ ̊ ı‡‡ÍÚÂËÒÚË ̃ÂÒÍÓ„Ó ÏÌÓ„Ó ̃ÎÂ̇,U0=En,On| ÒÓÓÚ‚ÂÚÒÚ‚ÂÌÌÓ Â‰ËÌË ̃̇ˇ Ë Í‚‡‰‡Ú̇ˇ ÌÛ΂‡ˇ χÚˈ ̊ ÔÓˇ‰Í‡n. “‡ÍËÏ Ó·‡ÁÓÏ, Î ̨·‡ˇ ÒÚÂÔÂÌ ̧ Í‚‡‰‡ÚÌÓÈ Ï‡Úˈ ̊UÔÓˇ‰Í‡nÔ‰ÒÚ‡‚Ëχ ‚ ‚ˉ ÎËÌÂÈÌÓÈ ÍÓÏ·Ë̇ˆËË Í‚‡‰‡ÚÌ ̊ı χÚˈUk,k=0, n−1. — Û ̃ÂÚÓÏ ̋ÚÓ„Ó ÂÁÛÎ ̧Ú‡Ú‡ ‰Ó͇Á‡ÌÓ
    Exact
    [12]
    Suffix
    , ̃ÚÓ Ï‡ÚË ̃̇ˇ ÙÛÌÍˆËˇf(U)ˇ‚ΡÂÚÒˇ ÎËÌÂÈÌÓÈ ÍÓÏ·Ë̇ˆËÂÈ Í‚‡‰‡ÚÌ ̊ı χÚˈUk,k=0, n−1: f(U) = n−1∑ k=0 αkUk, „‰Âαk,k= 0n−1, | ÌÂËÁ‚ÂÒÚÌ ̊ ÍÓ ̋ÙÙˈËÂÌÚ ̊, Û‰Ó‚ÎÂÚ‚Óˇ ̨ ̆Ë ÒËÒÚÂÏ ÎËÌÂÈÌ ̊ı ‡Î„·‡Ë ̃ÂÒÍËı Û‡‚ÌÂÌËÈ n−1∑ k=0 αkλkj=f(λj), j=1, n, ÂÒÎË ÒÓ·ÒÚ‚ÂÌÌ ̊ ̃ËÒ·λk,k= 0n−1, χÚˈ ̊U‡ÁÎË ̃Ì ̊.
    (check this in PDF content)

  14. Start
    8263
    Prefix
    −p 2(τ−η) cospL, α1= 1 pL e−p 2(τ−η) sinpL, „‰Â L=L(τ, η) =l(τ)−l(η).(17) “‡ÍËÏ Ó·‡ÁÓÏ, Ò Û ̃ÂÚÓÏ (16) ÂÁÓÎ ̧‚ÂÌÚ‡ Á‡‰‡ ̃Ë Ó ̄Ë (12) ËÏÂÂÚ ‚ˉ R(τ, η) =   cospLsinpL −sinpLcospL  e−p2(τ−η)(18) Ë, Òӄ·ÒÌÓ (15), (18), (13), (14) ΘC(p, τ) = ∫τ 0 e−p 2(τ−η) Q(η) cospLdη+ ∫τ 0 e−p 2(τ−η)[ psinpL−l′(η) cospL ] θ(0, η)dη.(19) — ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ÙÓÏÛÎ ̊ Ó·‡ ̆ÂÌˡ ÍÓÒËÌÛÒ-ÔÂÓ·‡ÁÓ‚‡Ìˡ ‘Û ̧Â
    Exact
    [10,11]
    Suffix
    θ(x, τ) = 2 π +∞∫ 0 ΘC(p, τ) cos(px)dp Ë Ô‰ÒÚ‡‚ÎÂÌˡ (19) ÔÓÒΠËÁÏÂÌÂÌˡ ÔÓˇ‰Í‡ ËÌÚ„ËÓ‚‡Ìˡ ÔÓÎÛ ̃‡ÂÏ: θ(x, τ) = 2 π ∫τ 0 {+∞∫ 0 e−p 2(τ−η) cospLcospx dp } Q(η)dη+ + 2 π ∫τ 0 {+∞∫ 0 e−p 2(τ−η) [ psinpLcospx−l′(η) cospLcospx ] dpθ(0, η)dη.(20) ¬ÌÛÚÂÌÌË ÌÂÒÓ·ÒÚ‚ÂÌÌ ̊ ËÌÚ„‡Î ̊ ‚ Ô‡‚ÓÈ ̃‡ÒÚË ‡‚ÂÌÒÚ‚‡ (20) ÏÓ„ÛÚ · ̊Ú ̧ ‚ ̊ ̃ËÒÎÂÌ ̊ ‡Ì‡ÎËÚË ̃ÂÒÍË.
    (check this in PDF content)

  15. Start
    8779
    Prefix
    (x, τ) = 2 π ∫τ 0 {+∞∫ 0 e−p 2(τ−η) cospLcospx dp } Q(η)dη+ + 2 π ∫τ 0 {+∞∫ 0 e−p 2(τ−η) [ psinpLcospx−l′(η) cospLcospx ] dpθ(0, η)dη.(20) ¬ÌÛÚÂÌÌË ÌÂÒÓ·ÒÚ‚ÂÌÌ ̊ ËÌÚ„‡Î ̊ ‚ Ô‡‚ÓÈ ̃‡ÒÚË ‡‚ÂÌÒÚ‚‡ (20) ÏÓ„ÛÚ · ̊Ú ̧ ‚ ̊ ̃ËÒÎÂÌ ̊ ‡Ì‡ÎËÚË ̃ÂÒÍË. ¬ÓÒÔÓÎ ̧ÁÓ‚‡‚ ̄ËÒ ̧ ËÁ‚ÂÒÚÌ ̊ÏË ÙÓÏÛ·ÏË ÚË„ÓÌÓÏÂÚËË cospLcospx= 1 2 [ cos(pL−x)+cos(pL+x) ] ,sinpLcospx= 1 2 [ sin(pL−x)+sin(pL+x) ] Ë ‡‚ÂÌÒÚ‚‡ÏË
    Exact
    [14]
    Suffix
    +∞∫ 0 e−αp 2 cosβp dp= √ π 2 √ α e−β 2/4α , +∞∫ 0 pe−αp 2 sinβp dp= β √ π 4α √ α e−β 2/4α , ÔˉÂÏ Í ÒÓÓÚÌÓ ̄ÂÌË ̨ θ(x, τ) = ∫τ 0 K(τ, η, x)θ(0, η)dη+ Ψ(τ, x),(21) „‰Â K(τ, η, x) = 1 2 √ π √ τ−η    1 2(τ−η) [ (L−x)e −(L−x) 2 4(τ−η)+ (L+x)e− (L+x)2 4(τ−η) ] − −l′(η) [ e −(L−x) 2 4(τ−η)+e− (L+x)2 4(τ−η) ]    ,(22) Ψ(τ, x) = 1 √ π ∫τ 0 1 2 √ τ−η [ e − (L−x)2 4(τ−η)+e− (L+x)2 4(τ−η) ] Q(η)dη.
    (check this in PDF content)

  16. Start
    9845
    Prefix
    ¿Ì‡ÎËÁ ÒÓÓÚÌÓ ̄ÂÌˡ (23) ÔÓ͇Á ̊‚‡ÂÚ, ̃ÚÓ ÙÛÌÍˆËˇu(τ)ˇ‚ΡÂÚÒˇ  ̄ÂÌËÂÏ ËÌÚ„‡Î ̧ÌÓ„Ó Û‡‚ÌÂÌˡ ¬ÓÎ ̧ÚÂ‡ ‚ÚÓÓ„Ó Ó‰‡, ˇ‰Ó(τ−η)−1/2A(τ, η)ÍÓÚÓÓ„Ó ËÏÂÂÚ Ò··Û ̨ ÓÒÓ·ÂÌÌÓÒÚ ̧ Ë Ì ˇ‚ΡÂÚÒˇ Ù‰„ÓÎ ̧ÏÓ‚ÒÍËÏ
    Exact
    [15]
    Suffix
    . ƒÎˇ ̃ËÒÎÂÌÌÓ„Ó  ̄ÂÌˡ Û‡‚ÌÂÌˡ (23) ‚ ̊·Ë‡ÂÏ ‰ÓÒÚ‡ÚÓ ̃ÌÓ ·ÓÎ ̧ ̄Ó ̇ÚÛ‡Î ̧ÌÓ ̃ËÒÎÓN, ÔÓ·„‡ÂÏ su= τ∗ N , τj=jsu, j=0, N ,(26) Ë ÒÚÓËÏ ËÚÂ‡ˆËÓÌÌ ̊È ÔÓˆÂÒÒ, ÔÓÁ‚ÓΡ ̨ ̆ËÈ ÔÓ ËÁ‚ÂÒÚÌ ̊Ï Á̇ ̃ÂÌËˇÏ ( u(τj) )m j=0 ËÒÍÓÏÓ„Ó  ̄ÂÌˡu(τ)Ò Á‡‰‡ÌÌÓÈ ÚÓ ̃ÌÓÒÚ ̧ ̨ ‚ ̊ ̃ËÒÎËÚ ̧ Á̇ ̃ÂÌËÂu(τm+1). œË ̋ÚÓÏτ0= 0Ëu(0) = 0. œÛÒÚ ̧ ‰‡Î uj=u(τj), φj=φ(τj), j=0, N .(27) “Ó„‰‡, Òӄ·ÒÌÓ (23),
    (check this in PDF content)

  17. Start
    10496
    Prefix
    „Ó  ̄ÂÌˡu(τ)Ò Á‡‰‡ÌÌÓÈ ÚÓ ̃ÌÓÒÚ ̧ ̨ ‚ ̊ ̃ËÒÎËÚ ̧ Á̇ ̃ÂÌËÂu(τm+1). œË ̋ÚÓÏτ0= 0Ëu(0) = 0. œÛÒÚ ̧ ‰‡Î uj=u(τj), φj=φ(τj), j=0, N .(27) “Ó„‰‡, Òӄ·ÒÌÓ (23), (24), (25) um+1= τm+1∫ 0 A(τm+1, η) √ τm+1−η u(η)dη+φm+1.(28) »ÌÚ„‡Î, ÒÚÓˇ ̆ËÈ ‚ Ô‡‚ÓÈ ̃‡ÒÚË ‡‚ÂÌÒÚ‚‡ (28), ˇ‚ΡÂÚÒˇ ÌÂÒÓ·ÒÚ‚ÂÌÌ ̊Ï, ̃ÚÓ ‰Â·ÂÚ Ì‚ÓÁÏÓÊÌ ̊Ï ÌÂÔÓÒ‰ÒÚ‚ÂÌÌÓ ËÒÔÓÎ ̧ÁÓ‚‡ÌË ËÁ‚ÂÒÚÌ ̊ı Í‚‡‰‡ÚÛÌ ̊ı ÙÓÏÛÎ
    Exact
    [16,17]
    Suffix
    . ƒÎˇ ÔÂÓ‰ÓÎÂÌˡ ̋ÚÓ„Ó Á‡ÚÛ‰ÌÂÌˡ ÔÓ·„‡ÂÏ Jm+1= τm+1∫ 0 A(τm+1, η) √ τm+1−η u(η)dη=J (1) m+1+J (2) m+1,(29) J (1) m+1= ∫τm 0 A(τm+1, η) √ τm+1−η u(η)dη,(30) J (2) m+1= τm+1∫ τm A(τm+1, η) √ τm+1−η u(η)dη,(31) „‰Â ËÌÚ„‡ÎJ (1) m+1ˇ‚ΡÂÚÒˇ ÒÓ·ÒÚ‚ÂÌÌ ̊Ï Ë Â„Ó Á̇ ̃ÂÌË ÏÓÊÂÚ · ̊Ú ̧ ‚ ̊ ̃ËÒÎÂÌÓ Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ËÁ‚ÂÒÚÌÓÈ Í‚‡‰‡ÚÛÌÓÈ ÙÓÏÛÎ ̊ Ú‡ÔˆËÈ [16] Ë ‡‚ÂÌÒÚ‚ (26), (27): J (1) m+1≈ √ su
    (check this in PDF content)

  18. Start
    10827
    Prefix
    ÌË ËÁ‚ÂÒÚÌ ̊ı Í‚‡‰‡ÚÛÌ ̊ı ÙÓÏÛÎ [16,17]. ƒÎˇ ÔÂÓ‰ÓÎÂÌˡ ̋ÚÓ„Ó Á‡ÚÛ‰ÌÂÌˡ ÔÓ·„‡ÂÏ Jm+1= τm+1∫ 0 A(τm+1, η) √ τm+1−η u(η)dη=J (1) m+1+J (2) m+1,(29) J (1) m+1= ∫τm 0 A(τm+1, η) √ τm+1−η u(η)dη,(30) J (2) m+1= τm+1∫ τm A(τm+1, η) √ τm+1−η u(η)dη,(31) „‰Â ËÌÚ„‡ÎJ (1) m+1ˇ‚ΡÂÚÒˇ ÒÓ·ÒÚ‚ÂÌÌ ̊Ï Ë Â„Ó Á̇ ̃ÂÌË ÏÓÊÂÚ · ̊Ú ̧ ‚ ̊ ̃ËÒÎÂÌÓ Ò ËÒÔÓÎ ̧ÁÓ‚‡ÌËÂÏ ËÁ‚ÂÒÚÌÓÈ Í‚‡‰‡ÚÛÌÓÈ ÙÓÏÛÎ ̊ Ú‡ÔˆËÈ
    Exact
    [16]
    Suffix
    Ë ‡‚ÂÌÒÚ‚ (26), (27): J (1) m+1≈ √ su 2 [ 2 m−2∑ j=1 A(τm+1, τj) √ m−j+ 1 uj+A(τm+1, τm)um ] .(32) «‡ÏÂÌÓÈη=τm+1−v2ÔÂÂÏÂÌÌÓÈ ËÌÚ„ËÓ‚‡Ìˡ ÌÂÒÓ·ÒÚ‚ÂÌÌ ̊È ËÌÚ„‡ÎJ (2) m+1, ÓÔ‰ÂÎÂÌÌ ̊È ‚ (31), Ò‚Ó‰ËÚÒˇ Í ËÌÚ„‡ÎÛ ÓÚ ÙÛÌ͈ËË, ËÏ ̨ ̆ÂÈ ÛÒÚ‡ÌËÏ ̊È ‡Á ̊‚. œÓ ̋ÚÓÏÛ Ò Û ̃ÂÚÓÏ (26), (27) J (2) m+1= 2 √s ∫u 0 A(τm+1, τm+1−v2)u(τm+1−v2)dv≈ ≈ √ su [ A(τm+1, τm+1)um+1+A(τm+1, τm)um ] ,(33) „‰Â ÔÓ‰
    (check this in PDF content)

  19. Start
    11996
    Prefix
    1) × ×   3 2 A(τm+1, τm)um+ m−1∑ j=1 A(τm+1, τj) √ m−j+ 1 uj  , m=1, N−1.(36) œË ̋ÚÓÏ ÒΉÛÂÚ Á‡ÏÂÚËÚ ̧, ̃ÚÓ ̋ÚË ‡‚ÂÌÒÚ‚‡ ËÏ ̨Ú ÒÏ ̊ÒÎ ÎË ̄ ̧ ÔË ‚ ̊ÔÓÎÌÂÌËË ÛÒÎӂˡ su< 1 max 06τ6τ∗ ( A(τ, τ) )2= 4π max 06τ6τ∗ ( l′(τ−0) )2.(37) ¬ÂÎË ̃Ë̇, ÒÚÓˇ ̆‡ˇ ‚ Ô‡‚ÓÈ ̃‡ÒÚË (37), Á‡‚ËÒËÚ ÎË ̄ ̧ ÓÚ ÒÍÓÓÒÚË ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ Ë ÏÓÊÂÚ ‡ÒÒχÚË‚‡Ú ̧Òˇ Í‡Í ‡Ì‡ÎÓ„ Ô‡‡ÏÂÚ‡ Û‡ÌÚ‡
    Exact
    [18]
    Suffix
    . 3. –ÂÁÛÎ ̧Ú‡Ú ̊ Ë Ëı Ó·ÒÛʉÂÌË –‡ÒÒÏÓÚËÏ ÌÂÍÓÚÓ ̊ ÂÁÛÎ ̧Ú‡Ú ̊ ËÒÒΉӂ‡ÌËÈ, ÓÚ‡Ê‡ ̨ ̆Ë ̇˷ÓΠı‡‡ÍÚÂÌ ̊ ÓÒÓ·ÂÌÌÓÒÚË ÔÓˆÂÒÒ‡ ÙÓÏËÓ‚‡Ìˡ ÚÂÏÔÂ‡ÚÛÌÓ„Ó ÔÓÙËΡθ(0, τ)̇ ‰‚ËÊÛ ̆ÂÈÒˇ ÔÓ Á‡‰‡ÌÌÓÏÛ Á‡ÍÓÌÛ „‡Ìˈ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡, ÍÓÚÓÓ ÔÓ‰‚ÂÊÂÌÓ ‚ÓÁ‰ÂÈÒÚ‚Ë ̨ ‚Ì ̄ÌÂ„Ó ÚÂÔÎÓ‚Ó„Ó ÔÓÚÓ͇.
    (check this in PDF content)

  20. Start
    13257
    Prefix
    ¿Ì‡ÎËÁ „‡ÙË ̃ÂÒÍÓÈ ËÌÙÓχˆËË ÔÓÁ‚ÓΡÂÚ Ò‰ÂÎ‡Ú ̧ ‚ ̊‚Ó‰ Ó ÚÓÏ, ̃ÚÓ ‚ Ó·ÓËı ÒÎÛ ̃‡ˇı ÚÂÏÔÂ‡ÚÛ‡ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ËÏÂÂÚ ‡ÒËÏÔÚÓÚË ̃ÂÒÍÓ Á̇ ̃ÂÌË θ(0, τ)∼ Q lim τ→+∞ l′(τ) , ̃ÚÓ ÔÓÎÌÓÒÚ ̧ ̨ Òӄ·ÒÛÂÚÒˇ Ò ÂÁÛÎ ̧Ú‡Ú‡ÏË, ÔÓÎÛ ̃ÂÌÌ ̊ÏË ‚ ‡·ÓÚÂ
    Exact
    [8]
    Suffix
    . ÓÏ ÚÓ„Ó, ÏÓÊÌÓ Á‡ÏÂÚËÚ ̧, ̃ÚÓ · ́ÓÎ ̧ ̄Ë Á̇ ̃ÂÌˡ ÒÍÓÓÒÚË ‰‚ËÊÂÌˡ „‡Ìˈ ̊ ÔË‚Ó‰ˇÚ Í ÒÓÍ‡ ̆ÂÌË ̨ ‚ÂÏÂÌË ÔÂÂıÓ‰ÌÓ„Ó ÔÓˆÂÒÒ‡ ÓÚθ(0,0) = 0‰Ó θ(0, τ)≈ Q lim τ→+∞ l′(τ) . ƒÎˇ ËÒΉӂ‡Ìˡ ÔÓˆÂÒÒ‡ ̋‚ÓÎ ̨ˆËË ÚÂÏÔÂ‡ÚÛ ̊ ‰‚ËÊÛ ̆ÂÈÒˇ „‡Ìˈ ̊ ÔÓÎÛÔÓÒÚ‡ÌÒÚ‚‡ ‚ ÛÒÎӂˡı ̇„‚‡ ÌÂÒÚ‡ˆËÓ̇Ì ̊Ï ‚Ì ̄ÌËÏ ÔÓÚÓÍÓÏ · ̊· ‚ ̊·‡Ì‡ ÔÂËÓ‰Ë ̃ÂÒ͇ˇ Á‡‚ËÒËÏÓÒÚ ̧Q(τ) = 1+sinπτÏÓ ̆ÌÓÒÚË ÔÓÚÓ͇, „‡ÙËÍ
    (check this in PDF content)