İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi

1305-7820 2587-165X

İstanbul Ticaret Üniversitesi

10.55071/ticaretfbd.1391212

Partial Differential Equations

Kısmi Diferansiyel Denklemler

FAST DIFFUSION EQUATIONS AND SOME INTEGRAL INEQUALITIES RELATED TO GREINER OPERATOR

GREINER OPERATÖRÜYLE İLİŞKİLENDİRİLMİŞ HIZLI DİFÜZYON DENKLEMİ VE BAZI İNTEGRAL EŞİTSİZLİKLERİ

https://orcid.org/0000-0002-5684-2309

Utku

Ahmet Uğur

ISTANBUL COMMERCE UNIVERSITY

https://orcid.org/0000-0002-9349-5166

Yener

Abdullah

ISTANBUL COMMERCE UNIVERSITY

06 26 2024

23 45 14 26 11 15 2023 04 03 2024

2002

İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi

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)=0𝑢(𝜔,0) = 𝑢$(𝜔) ≥ 0in 𝛺×(0,𝑇),on 𝜕𝛺×(0,𝑇), in 𝛺.Here, 0<𝑚<1, 𝑉∈𝐿%&'(𝛺), 0<𝐴(𝜔)∈ 𝐿%&'(𝛺)andΩ is abounded 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.

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$(𝜔) ≥ 0,𝜕𝑢 " " 𝜕𝑡 =∇! ∙(𝐴(𝜔)∇!𝑢 )+𝑉(𝜔)𝑢!𝑢(𝜔,𝑡)=0𝑢(𝜔,0) = 𝑢$(𝜔) ≥ 0in 𝛺×(0,𝑇),on 𝜕𝛺×(0,𝑇), in 𝛺.""𝛺×(0,𝑇),𝜕𝛺 × (0, 𝑇), 𝛺doğrusal 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.

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

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

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