Global Existence of Solutions to a Chemotaxis System With Nonlinear Neumann Boundary Condition

ABSTRACT We consider the classical solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary conditions () in a smooth bounded domain , where and . Under certain conditions, we show the global existence of a classical solution for the above system with nonlinear Neumann boundary conditions and subcritical growth rates for the boundary. In particular, we remove the convexity assumption of the domain and relax the range of .