TIME-GLOBAL EXISTENCE OF RADIAL SOLUTIONS TO A PARABOLIC-ELLIPTIC SYSTEM RELATED TO CHEMOTAXIS

We study the time-global existence of radial solutions to a parabolic-elliptic system related to a biological model. The model describes chemotactic aggregation of cellular slime molds which move preferentially towards relatively high concentrations of a chemical secreted by the amoebae themselves. In the model, the relation between the movement of cells and the chemical concentration is represented by the chemotaxis coe‰cient. The behavior of solutions is determined by the chemotaxis coe‰cient and the initial function. In the present paper, we investigate the relation among the behavior of the solution, the chemotaxis coe‰cient and the initial function. 1