O‘ZGARUVCHAN KOEFFITSIYENTLI ISSIQLIK O‘TKAZUVCHANLIK TENGLAMASI UCHUN VAQT BO‘YICHA TESKARI MASALANING SHARTLI TURG‘UNLIGI VA REGULYARLASHGAN YECHIMI
Аннотация
Ushbu maqolada o‘zgaruvchan koeffitsiyentli issiqlik o‘tkazuvchanlik tenglamasi uchun vaqt bo‘yicha teskari masala o‘rganilgan. Masalaning fizik va matematik mohiyati tahlil qilinib, uning Hadamard ma’nosida korrekt bo‘lmagan masalalar sinfiga mansubligi ko‘rsatildi. Ishda mos Shturm–Liuvill spektral masalasi sonli usullar asosida yechildi hamda Furye usuli yordamida rasmiy yechim hosil qilindi. Teskari masalaning yagonaligi isbotlanib, Tixonov korrektlik to‘plamida shartli turg‘unlik bahosi olindi. Shuningdek, Tixonov regulyarlash usuli va spektrni chekli kesish usuli asosida turg‘un regulyarlashgan yechimlar qurildi.
Библиографические ссылки
Tikhonov A.N., Arsenin V.Y. Solutions of Ill-posed Problems. New York: Wiley, 1977.
Lavrentiev M.M., Romanov V.G., Shishatskii S.P. Ill-posed Problems of Mathematical Physics and Analysis. American Mathematical Society, 1986.
Samarskii A.A., Vabishchevich P.N. Numerical Methods for Solving Inverse Problems of Mathematical Physics. De Gruyter, 2007.
Isakov V. Inverse Problems for Partial Differential Equations. Springer, 2006.
Alifanov O.M. Inverse Heat Transfer Problems. Springer, 1994.
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