On a Parabolic-ODE system of chemotaxis

Mihaela Negreanu, J. Ignacio Tello
2018 Discrete and Continuous Dynamical Systems. Series S  
In this article we consider a coupled system of differential equations to describe the evolution of a biological species. The system consists of two equations, a second order parabolic PDE of nonlinear type coupled to an ODE. The system contains chemotactic terms with constant chemotaxis coefficient describing the evolution of a biological species "u" which moves towards a higher concentration of a chemical species "v" in a bounded domain of R n . The chemical "v" is assumed to be a
more » ... e substance or with neglectable diffusion properties, satisfying the equation We obtain results concerning the bifurcation of constant steady states under the assumption hv + χuhu > 0 with growth terms g. The Parabolic-ODE problem is also considered for the case hv + χuhu = 0 without growth terms, i.e. g ≡ 0. Global existence of solutions is obtained for a range of initial data.
doi:10.3934/dcdss.2020016 fatcat:uxyeu5q46ffjlj7myk44r52wji