Global Boundedness and Mass Persistence of Solutions to A Chemotaxis-Competition System with Logistic Source

Year 2025, Volume: 29 Issue: 1, 167 - 175, 25.04.2025

Halil İbrahim Kurt

https://doi.org/10.19113/sdufenbed.1627078

Abstract

This article examines the population dynamics of solutions such as global existence, global boundedness, and mass persistence, to a parabolic elliptic type of chemotaxis-competition system including logistics kinetics in a smooth bounded domain. Tello and Winkler were the first to investigate the global existence and global boundedness of the system mentioned above. Then Tao and Winkler examined qualitative properties of the given system such as the mass persistence of solutions. This study improves some known results and reveals that under some suitable conditions, there exists a classical solution to the system described above that is globally bounded. In addition, it is shown that the population as a whole is never extinct.

Keywords

Regular sensitivity, Logistic source, Global existence, Global boundedness, Mass persistence

Thanks

I appriciate all your time and consideration. Best Regards, Halil İbrahim Kurt

Bir Lojistik Kemotaksis-Rekabet Sisteminin Çözümlerinin Küresel Sınırlılığı ve Kitlesel Kalıcılığı

Abstract

Bu makale, düzgün sınırlı bir alanda lojistik kinetik içeren parabolik eliptik tipte bir kemotaksi-rekabet sistemine ait global varlık, global sınırlılık ve kütlesel kalıcılığı gibi çözümlerin popülasyon dinamiklerini incelemektedir. Tello ve Winkler'in ilk olarak yukarıda belirtilen sistemin küresel varlığını ve sınırlılığını incelemiştir. Daha sonra Tao ve Winkler, verilen sistemin çözümlerin kütlesel kalıcılığı gibi dinamik özelliklerini araştırmışlardır. Bu çalışmada, bilinen bazı sonuçlar geliştirilmiştir ve uygun koşullar altında sistemin küresel olarak var ve sınırlı olan tek bir klasik çözüme sahip olduğunu göstermiştir. Buna ilave olarak, popülasyonun bir bütün olarak asla yok olmadığı gösterilmiştir.

Keywords

Lineer hassasiyet, Lojistik kaynak, Global varlık, Global sınırlılık, Kitlesel kalıcılık

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