FAST DIFFUSION EQUATIONS AND SOME INTEGRAL INEQUALITIES RELATED TO GREINER OPERATOR

Yıl 2024, Cilt: 23 Sayı: 45 , 14 - 26 , 26.06.2024

Ahmet Uğur Utku , Abdullah Yener

https://doi.org/10.55071/ticaretfbd.1391212

https://izlik.org/JA92ER94LS

Öz

The primary goal of this article is to investigate nonexistence of positive solutions to the following nonlinear parabolic problem:𝜕𝑢 " " 𝜕𝑡 =∇! ∙(𝐴(𝜔)∇!𝑢 )+𝑉(𝜔)𝑢
!𝑢(𝜔,𝑡)=0
𝑢(𝜔,0) = 𝑢$(𝜔) ≥ 0
in 𝛺×(0,𝑇),
on 𝜕𝛺×(0,𝑇), in 𝛺.
Here, 0<𝑚<1, 𝑉∈𝐿%&'(𝛺), 0<𝐴(𝜔)∈ 𝐿%&'(𝛺)andΩ is a
bounded domain with smooth boundary in Carnot-Carathéodory space related with the Greiner vector fields.
Another aim of this article is to obtain some Hardy type inequalities with non-radial weights related to Greiner operator.

Anahtar Kelimeler

Fast diffusion equation , Greiner operator , Hardy type inequalities , nonexistence of positive solutions.

GREINER OPERATÖRÜYLE İLİŞKİLENDİRİLMİŞ HIZLI DİFÜZYON DENKLEMİ VE BAZI İNTEGRAL EŞİTSİZLİKLERİ

https://izlik.org/JA92ER94LS

Öz

Bu makalenin öncelikli amacı, Greiner vektör alanlarıyla ilişkilendirilmiş Carnot-Carathéodory uzayındaki düzgün sınırlara sahip sınırlı bir Ω bölgesinde,
Abstract
𝜕𝑢
!𝜕𝑡 =∇! ∙(𝐴(𝜔)∇!𝑢 )+𝑉(𝜔)𝑢 ,
𝑢(𝜔, 𝑡) = 0,
𝑢(𝜔,0) = 𝑢$(𝜔) ≥ 0,
𝜕𝑢 " " 𝜕𝑡 =∇! ∙(𝐴(𝜔)∇!𝑢 )+𝑉(𝜔)𝑢
!𝑢(𝜔,𝑡)=0
𝑢(𝜔,0) = 𝑢$(𝜔) ≥ 0
in 𝛺×(0,𝑇),
on 𝜕𝛺×(0,𝑇), in 𝛺.
""
𝛺×(0,𝑇),
𝜕𝛺 × (0, 𝑇), 𝛺
doğrusal olmayan parabolik probleminin pozitif çözümünün
( yokluğunun araştırılmasıdır. Burada, 0 < 𝑚 < 1, 𝑉 ∈ 𝐿%&'(𝛺) ve
(
0 < 𝐴(𝜔) ∈ 𝐿%&'(𝛺)’dır.
Bu makalenin diğer bir amacı ise Greiner operatörü ile ilişkilendirilmiş radyal olmayan ağırlıklı bazı Hardy tipi eşitsizlikler elde etmektir.

Anahtar Kelimeler

Greiner operatör , Hardy tipi eşitsizlikler , hızlı difüzyon denklemi , pozitif çözümün yokluğu.

Kaynakça

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