Li simmetriyasi tahlili, giperbolik sistemalarning Lyapunov bo‘yicha turg‘unligini tahlil qilish va modellashtiri.

Ilmiy rahbari: Aloev Raxmatillo Juraevich
Bajarilish muddati: 04.01.2021-31.12.2023
Loyiha shifri: UZB-Ind-2021-87
Loyiha turi: Amaliy

Kutilayotgan natijalar va ularning ahamiyati: Li guruhi metodi yordamida invariantlik holati, Li simmetriyasi tahlili, cheksiz kichik simmetriyalarning Li algebrasi, simmetrik o‘zgaruvchilar va kvazichiziqli giperbolik sistemalarning simmetrik echimlarini tadqiq etish. Bundan tashqari, tadqiqot natijalarini samarali tarzda taqdim etish va grafik tasvirlar orqali tushuntirish. Li guruhi hamda giperbolik sistemalarning Lyapunov turg‘unligini tahlil qilish asosida sonli algoritmlar ishlab chiqish. Shuningdek, ushbu sonli usullar yordamida aniq natijalarni o‘rganish uchun olingan natijalarni tahlil qilish. Loyiha doirasida kvazichiziqli giperbolik tenglamalar sistemasi uchun aralash masalaning aniq echimlari va eksponentsial turg‘un sonli echimini topish uchun Li simmetriyasi tahlili va adekvat hisoblash modeli ishlab chiqish. Li simmetriyasi tahlili va ishlab chiqilgan adekvat hisoblash modelidan beton qoplamasiz sug‘orish kanallarining sug‘orish tizimlarida suv harakatini boshqarishda foydalanish. Li simmetriyasini tahlil qilish va kvazichiziqli giperbolik sistemalarning aralash masalalarini aniq va taqribiy echish uchun adekvat hisoblash modellarini qurish. Binobarin, hisoblash modellari uchun Lyapunov bo‘yicha ayirmali sxemaning turg‘unligini isbotlash.
Hisobot davrida (loyiha yakunida) qo‘lga kiritilgan muhim natijalar: Bir o‘lchovli chiziqli simmetrik giperbolik sistemalarga qo‘yilgan aralash masalalar bilan ifodalanadigan jarayonlarni tahlil qilindi. O‘zbekiston sharoitida olingan gidrologik va meteorologik ma’lumotlar asosida ushbu masalalarni echishga doir ma’lumotlarni to‘plandi hamda to‘plangan ma’lumotlar umumlashtirilib, birlamchi qayta ishlandi. O‘zgaruvchan koeffitsientli giperbolik sistemalarning turg‘un echimlarini topish uchun ayirmali sxemalar qurildi va ularning turg‘unligini isbot qilinib Saint Venant tenglamalarini turg‘un echimlarini topish uchun ayirmali sxemalar tadqiq etildi. Turg‘unligi isbot qilingan sxemalar ustida hisoblash eksperementlari o‘tkazilib, olingan natijalarni vizualizatsiya qilindi. Olingan natijalar nazariy va amaliy xarakterga ega bo‘lib, kelgusida giperbolik sistemalarga qo‘yilgan aralash masalalar uchun ayirmali sxema nazariyasini rivojlantirish uchun xizmat qiladi. Shuningdek elektr energiyasi transporti, ochiq kanallarda suyuqlik oqimi, optik tolalarda yorug‘likning tarqalishi kabi masalalarini sonli echishda qo‘llanilishi mumkin.
Patent

Loyiha doirasida chop WoS va Scopus bazasidagi xalqaro ilmiy ishlar

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