Methods and Applications of Analysis

Volume 12 (2005)

Number 3

Structure of Solutions to a Chemotaxis System in One Space Dimension

Pages: 221 – 238

DOI: http://dx.doi.org/10.4310/MAA.2005.v12.n3.a1

Author

Toshitaka Nagai

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

35B40, 35M10, 92C17

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