Methods and Applications of Analysis

Volume 12 (2005)

Number 3

Structure of Solutions to a Chemotaxis System in One Space Dimension

Pages: 221 – 238



Toshitaka Nagai


We consider a chemotaxis system consisting of one parabolic equation and one ordinary differential equation in one space dimension with a logarithmic chemotactic sensitivity function and the exponential growth of dynamics for the chemical attractant. The structure of positive solutions is studied from the viewpoint of infinite-dimensional dynamical systems.


Chemotaxis system; structure of solutions; exact solution; invariant manifold

2010 Mathematics Subject Classification

35B40, 35M10, 92C17

Published 1 January 2005