Dissipative Gradient Nonlinearities Prevent δ$\delta$ ‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models

By Tongxing Li, Daniel Acosta-Soba, A. Columbu, Giuseppe Viglialoro. Studies in applied mathematics (Cambridge), 2024

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We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density u$u$ , the chemosensitivities and the production rates of the chemoattractant v$v$ and the chemorepellent w$w$ . In addition, a source involving also the gradient of u$u$ is incorporated. Our overall study touches on different aspects: we address questions connected to local well‐posedness, we derive sufficient conditions to ensure boundedness of solutions, and finally, we develop numerical simulations giving insights into the evolution of the system.

Subfields: Biomedical Engineering, Cell Biology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/0123350a147938b1520e8a8db8831d54c5bbb3d5