On a parabolic-elliptic Keller–Segel system with nonlinear signal production and nonlocal growth term

This paper focuses on a parabolic-elliptic Keller-Segel system with nonlinear signal production and nonlocal growth term• When χ > 0, the solution of the above system is global and uniformly bounded, if the parameters satisfy certain suitable assumptions.• When χ < 0, the system possesses a globally bounded classical solution, provided that a 1 > a 2 |Ω|.These results indicate that the repulsive mechanism plays a crucial role in ensuring the global boundedness of solutions.In addition, the paper derives the large time behavior of globally bounded solutions for the chemo-attractive or chemo-repulsive system by constructing energy functionals.Contents 1. Introduction 62 2. Preliminaries 64 3. Global boundedness when χ > 0 6 4 4. Global boundedness when χ < 0 6 9 5. Large time behavior 71 6. Acknowledgements 75 References 75