Global existence and boundedness of solutions of a chemotaxis system with logistic source

Abstract:

The properties of solutions of a class of chemotaxis system with logistic source are considered. By using prior estimates and the decay properties of Neumann heat semigroup, it is proved that there exists a unique global classical solution for the homogenous Neumann initial value problem in three-dimensional bounded domain with smooth boundary if the quadratic coefficient of the logistic source is sufficiently large.