Refined criteria toward boundedness in an attraction–repulsion chemotaxis system with nonlinear productions (Q6607926)

In this paper, the authors investigate the zero-flux boundary value problem for an attraction-repulsion model with a nonlinear production rate. The authors first prove the local existence of classical solutions to the model, and further establish global solvability under various conditions, along with providing uniform boundedness estimates for the solutions. Finally, the research is complemented with numerical simulations in bi-dimensional domains.