Tek Tür, İki Kimyasal ve Tekillik İçeren Lojistik Bir Kemotaksi Sisteminde Süreklilik ve Sınırlılık

Öz

Kemotaksi sistemleri, biyolojik popülasyonların kimyasal gradyanlara tepkisini tanımlar; ancak tekil duyarlılıklar, matematiksel kararlılığı zorlaştıran patlama (blow-up) olgularına yol açabilmektedir. Bu çalışma, tek tür ve iki etkileşen kimyasal madde içeren, lojistik büyüme terimiyle desteklenmiş parabolik–eliptik–eliptik tipte bir kemotaksi modelini homojen Neumann sınır koşulları altında ele almaktadır. Patlamayı önleyen mekanizmaların belirlenmesi gerekliliğinden hareketle, klasik çözümlerin sürekliliği ve küresel sınırlılığı için yeterli koşullar titizlikle ortaya konmuştur. Özellikle, lojistik sönüm etkisi yeterince güçlü olduğunda sistemin zamana bağlı olarak pozitifliğini koruyan benzersiz ve küresel olarak sınırlı bir çözüme sahip olduğu kanıtlanmıştır. Bu bulgular, lojistik düzenlemenin tekil duyarlılığa rağmen kemotaktik birikimi nasıl dengelediğini ortaya koyarak önceki teorik sonuçları geliştirmektedir.

Anahtar Kelimeler

• Kemotaksi
• çok türlü sistem
• tekil duyarlılık
• küresel sınırlılık
• süreklilik

Persistence and boundedness in a logistics chemotaxis system including one-species, two-chemicals, and singularity

Öz

Chemotaxis systems describe how biological populations respond to chemical gradients, yet singular sensitivities often lead to blow-up phenomena that challenge mathematical stability. This study addresses a parabolic–elliptic–elliptic chemotaxis model involving one species and two interacting chemicals with a logistic growth term under homogeneous Neumann boundary conditions. Motivated by the need to identify mechanisms preventing blow-up, we establish rigorous conditions ensuring persistence and global boundedness of classical solutions. Specifically, it is proven that when the logistic damping effect is sufficiently strong, the system admits a unique global solution that remains positive and uniformly bounded over time. These findings advance previous theoretical results by clarifying how logistic regulation stabilizes chemotactic aggregation even under singular sensitivity.

Anahtar Kelimeler

• Chemotaxis
• multi-species system
• singular sensitivity
• global boundedness
• persistence

Kaynakça

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