Large-time behavior of a parabolic-parabolic chemotaxis model with logarithmic sensitivity in one dimension
The authors study a one-dimensional repulsive chemotaxis model with logarithmic sensitivity, consisting of two coupled nonlinear, second order parabolic equations for the cell density and the chemical concentration, subject to Neumann boundary conditions. Using a Lyapunov functional approach, they prove a global existence result for smooth positive initial data and characterize the long-term dynamics of solutions. Only constant positive steady states are shown to be possible.
scientific article; zbMATH DE number 6157331