A note on a periodic Parabolic-ODE chemotaxis system

• DOI: 10.1016/j.aml.2020.106351
• Publication Date: 2020-03-25T06:35:58Z
• Authors: Mihaela Negreanu; J. Ignacio Tello; Antonio M. Vargas
• Keywords: Ode; Logistic function; Reaction–diffusion system

Abstract Existence of global classical solutions with a certain periodic asymptotic behavior of a class of reaction diffusion systems with chemotactic terms is demonstrated. This class contains a system consisting of a parabolic equation with a logistic-like term describing the behavior of a biological species and an ordinary differential equation modeling the concentration of a chemical substance throughout a regular function h . The logistic-like term limits the growth of the biological species and it contains a carrying capacity with a time-periodic asymptotic behavior.