In this paper we consider a Keller-Segel-type chemotaxis model with reaction term under no-flux boundary conditions, where the kinetics term of the system is power function. Assuming some growth conditions, the existence of bounded global strong solution to the parabolic-parabolic system is given. We also give the numerical test and find out that there exists a threshold. When the power frequency greater than the threshold, both global solution and blow-up solution exist.
Chen, X., Hu, F., Zhang, J., & Shen, J. (2017). Global Existence and Blow-Up for a Chemotaxis System. Mathematical Modelling and Analysis, 22(2), 237-251. https://doi.org/10.3846/13926292.2017.1292323
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