We study large-time behavior of solutions to the initial-value problem for a parabolic system of chemotaxis in one space dimension. Chemotaxis is the directed movement of amoebae in response to chemical gradients. The aim of this paper is to obtain the first and second asymptotic profiles of solutions to the parabolic system. Then we are able to find out the optimal asymptotic rate of the first asymptotic profiles.
"Sharp asymptotics for a parabolic system of Chemotaxis in one space dimension." Differential Integral Equations 22 (1/2) 35 - 51, January/February 2009. https://doi.org/10.57262/die/1356038553