Dissipative Gradient Nonlinearities Prevent δ$\delta$‐Formations in Local and Nonlocal Attraction–Repulsion Chemotaxis Models
Tongxing Li, Daniel Acosta‐Soba, Alessandro Columbu, Giuseppe Viglialoro
Abstract
ABSTRACT We study a class of zero‐flux attraction–repulsion chemotaxis models, characterized by nonlinearities laws for the diffusion of the cell density , the chemosensitivities and the production rates of the chemoattractant and the chemorepellent . In addition, a source involving also the gradient of 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.
Topics & Concepts
AttractionDissipative systemChemotaxisDeltaPhysicsClassical mechanicsMathematical analysisMathematicsBiologyQuantum mechanicsBiochemistryAstronomyPhilosophyReceptorLinguisticsMathematical Biology Tumor GrowthSlime Mold and Myxomycetes ResearchMicrotubule and mitosis dynamics