Global existence results for coupled nonlinear parabolic equations with weighted coefficients
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Ushbu maqolada biz ikkita o‘zaro kuchli bog‘langan ta‘sirlashuvchi maydonlarning bog‘langan
dinamikasini tasvirlovchi og‘irlikli chiziqsiz parabolik tenglamalar sistemalar sinfini ko‘rib chiqamiz.
Energiya baholari va integral tengsizliklardan foydalanib, tegishli og‘irlikli Sobolev fazolarida kuchsiz
yechimlarning global mavjudligi uchun yetarli shartlar aniqlanadi. Shuningdek, yechimlarni samarali
yaqinlashtirish maqsadida Peaceman-Rachford sonli hisoblash usuli va Tomas algoritmi(haydash
usuli) asosida sonli sxema ishlab chiqiladi. Taklif etilgan hisoblash doirasi ikki va uch o‘chovli sonli
simulyatsiyalar yordamida, dinamik sirt grafigi va animatsiyalangan profillar bilan amalga oshiriladi
va namoyish etiladi. Natijalar global yechimning sifat jihatlarini ko‘rsatib beradi, analitik natijalarni
tasdiqlaydi hamda chiziqsiz diffuziya, og‘irlikli bir jinsli bo‘lmagan va komponentlararo bog‘lanish
o‘rtasidagi o‘zaro ta‘sir haqida qo‘shimcha tushuncha beradi.
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