IKKINCHI TARTIBLI DIFFERENTSIAL-OPERATOR TENGLAMA UCHUN QO'YILGAN KOSHI MASALASI YECHIMI HAQIDA

u t funktsiya t skalyar argumentning funktsiyasi bo‘lib, u qiymatlarini H-Gilbert fazosida qabul qilsin, ( ) f t va t skalyar argumentning funktsiyasi bo‘lib, u F- Gilbert fazosida qiymatlarini qabul qilsin, A va B operatorlar: : , : , ( ) ( ). A H F B H F D A D B    Ta’rif 1. Bu Au f    ko‘rinishidagi operator tip koeffitsientli tenglama ikkinchi tartibli differentsial-operator tenglama deyiladi. Ushbu Koshi masalasini qaraymiz: 1 0 (1) (0) , (0) (2) Bu Au u u u u         Bu yerda biz А operator simmetriyali va musbat, ya’ni , ( ) u D A    uchun ( , ) ( , ),( , ) ( , )( 0), Au u A Au u u u        1 B   va B-operatori simmetriyali, ya’ni ( , ) (u,B ) Bu    deb hisoblaymiz.

Keywords

Funktsiya, operator, yagonalik, turg'unlik, ikkinchi tartibli differentsial-operator tenglama, Koshi masalasi, Gilbert fazosi. функция, оператор, единственность, устойчивость, дифференциально-операторное уравнения второго порядка, задача Коши, Гильвертово пространство. the function, the operator, the uniqueness and stability, the second order of differential-operator equation, the Cauchy problems, the Gilbert space., Funktsiya, operator, yagonalik, turg'unlik, ikkinchi tartibli differentsial-operator tenglama, Koshi masalasi, Gilbert fazosi. функция, оператор, единственность, устойчивость, дифференциально-операторное уравнения второго порядка, задача Коши, Гильвертово пространство. the function, the operator, the uniqueness and stability, the second order of differential-operator equation, the Cauchy problems, the Gilbert space.

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