摘要
This work deals with the zero-Neumann boundary problem to a fully parabolic chemotaxis system with a nonlinear signal production function f（s） fulfilling 0 〈 f（s） 〈 Ksα for all s 〉 0, where K and α are positive parameters. It is shown that whenever 0 〈 α 〈 2/n （where n denotes the spatial dimension） and under suitable assumptions on the initial data, this problem admits a unique global classical solution that is uniformly-in-time bounded in any spatial dimension. The proof is based on some a priori estimate techniques.
This work deals with the zero-Neumann boundary problem to a fully parabolic chemotaxis system with a nonlinear signal production function f（s） fulfilling 0 〈 f（s） 〈 Ksα for all s 〉 0, where K and α are positive parameters. It is shown that whenever 0 〈 α 〈 2/n （where n denotes the spatial dimension） and under suitable assumptions on the initial data, this problem admits a unique global classical solution that is uniformly-in-time bounded in any spatial dimension. The proof is based on some a priori estimate techniques.
基金
Supported by the National Natural Science Foundation of China(11571070)
