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, vol.76, no.4, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 76 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.1007/s00033-025-02550-6
  • Journal Name: Zeitschrift fur Angewandte Mathematik und Physik
  • Journal Indexes: 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
  • Keywords: Chemotaxis, Global boundedness, Global existence, Logistic sources, Nonlinear boundary, Weak singular sensitivity
  • Karadeniz Technical University Affiliated: Yes

Abstract

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.