On a parabolic-elliptic chemotactic model with coupled boundary conditions (Q708551)

The author analyze a nonlinear system of parabolic-elliptic type whose origin is a model of chemotaxis. The parabolic equation describes the cell density and the elliptic equation describes the concentration of the chemoattractant or chemorepellant. The authors prove global (in time) existence and uniqueness of positive classical solutions. The authors also analyze the associated elliptic steady state problem. Under certain conditions on the parameters of the model, it is shown that there is a unique homogeneous equilibrium solution which is globally stable.