«FarDU ilmiy xabarlari» Volume 28 Issue 1 (2022)
SOHA CHEGARASIDA BUZILADIGAN PARABOLIK TENGLAMA UCHUN CHEGARAVIY MASALALAR
Urinov, Axmadjon, Уринов, Ахмаджон
Abstract
<p>Soha chegarasida buziladigan parabolik tenglama uchun chegaraviy masalalar bayon qilingan va o‘rganilgan. <br />Masala yechimining mavjudligi, yagonaligi va turg‘unligi isbotlangan.Masala yechimining yagonali energiya integrallar usuli bilan 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. Masala yechimining bahosi olingan, undan uning berilgan funksiyalarga doimiy bog‘liqligi isbotlangan.</p>
boundary value problemsparabolic type equationspectral methodGreen's functionintegral equation.boundary value problemsparabolic type equationspectral methodGreen's functionintegral equation.
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