Can logistic damping prevent blowup for weak singular sensitivity chemotaxis systems under nonlinear boundary conditions?

Le M., Bao L., KURT H. İ.

Zeitschrift fur Angewandte Mathematik und Physik, cilt.76, sa.4, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 4
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s00033-025-02550-6
  • Dergi Adı: Zeitschrift fur Angewandte Mathematik und Physik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Chemotaxis, Global boundedness, Global existence, Logistic sources, Nonlinear boundary, Weak singular sensitivity
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

This paper investigates the classical solutions of a chemotaxis system with weakly singular sensitivity, -∇uvk∇vfor k∈(0,1), and logistic sources under general nonlinear Neumann boundary conditions. Previous studies have shown that quadratic logistic damping can prevent blowup under homogeneous Neumann boundary conditions. Our work extends these results by proving that the logistic term, or even a sub-logistic term, is sufficiently strong to ensure global existence and boundedness of solutions, even under general boundary conditions that allow population influx into the domain.