«FarDU ilmiy xabarlari» Volume 29 Issue 1 (2023)
SOHA CHEGARASIDA BUZILADIGAN TO‘RTINCHI TENGLAMA UCHUN ARALASH MASALA
Mamanazarov, Azizibek, Usmonov, Doniyor
Abstract
<p><em>Ushbu maqolada to‘rtburchak sohada Kaputo ma’nosidagi kasr hosilasini o‘z ichiga olgan to‘rtinchi tartibli bitta buziladigan tenglama uchun boshlang'ich-chegaraviy masala bayon qilingan va o‘rganilgan. Masala yechimining mavjudligi va yagonaligi isbotlangan. O‘zgaruvchilarni ajratish usuli orqali, oddiy differensial tenglama uchun spektral masala hosil qilingan. Bu spektral masala Grin funksiyasi yordamida simmetrik yadroli ikkinchi tur Fredgolm integral tenglamasiga ekvivalent keltirilgan. O‘rganilayotgan masalaning yechimi spektral masalaning xos funksiyalar sistemasiga nisbatan Furye qatorining yig‘indisi sifatida topilgan.</em></p>
buziladigan to‘rtinchi tartibli tenglama; chegaraviy masala; spektral masala; Grin funksiyasi; integral tenglama; yechimning mavjudligi va yagonaligi.degenerate fourth order equation; initial-boundary value problem; spectral problem; Green's function; integral equation; еxistence and uniqueness of the solution.
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