Global stability of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions

Abstract

This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under suitable assumptions on the boundary data, solutions starting in $H^2$-space exist globally in time and the differences between the solutions and their corresponding boundary data converge to zero, as time goes to infinity. There is no smallness restriction on the magnitude of initial perturbations. Moreover, numerical simulations show that the assumptions on the boundary data are necessary for the above mentioned results.