Chemotaxis models with mixed mechanisms: boundedness in growth-dominated regimes

2025/07/27 by Li, Tongxing, Frassu, Silvia, Viglialoro, Giuseppe
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.20310

Abstract

We study a chemotaxis-growth system with nonlinear local and nonlocal reactions and gradient-dependent damping. Under suitable conditions on the system parameters and spatial dimension, we prove that solutions exist globally in time and remain uniformly bounded. Unlike classical cases, when local growth dominates, mass control is not automatic. To address this, we use a two-step approach: first ensuring bounded total mass, then establishing full uniform boundedness. The results highlight how chemotaxis, damping, and nonlocal effects interact to prevent blow-up in structured models.

Citations

• Dissipation through combinations of nonlocal and gradient nonlinearities in chemotaxis models
• Dissipative gradient nonlinearities prevent δ-formations in local and nonlocal attraction-repulsion chemotaxis models
• Boundedness through nonlocal dampening effects in a fully parabolic chemotaxis model with sub and superquadratic growth
• A Keller-Segel type taxis model with ecological interpretation and boundedness due to gradient nonlinearities
• Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model
• LOWER ESTIMATE OF THE ATTRACTOR DIMENSION FOR A CHEMOTAXIS GROWTH SYSTEM

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