GREINER OPERATÖRÜYLE İLİŞKİLENDİRİLMİŞ HIZLI DİFÜZYON DENKLEMİ VE BAZI İNTEGRAL EŞİTSİZLİKLERİ

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

Ahmet Uğur Utku , Abdullah Yener

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

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.

FAST DIFFUSION EQUATIONS AND SOME INTEGRAL INEQUALITIES RELATED TO GREINER OPERATOR

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.

Kaynakça

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