Structure of Solutions to a Chemotaxis System in One Space Dimension

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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Published 1 January 2005