Global existence, boundedness and asymptotic behavior to a chemotaxis model with singular sensitivity and logistic source

Abstract

ABSTRACT This article deals with the chemotaxis model with singular sensitivity and logistic source under homogenous Neumann boundary condition in a smooth bounded domain , with and for all s>0 with . For , we show that the system admits a global classical solution that provides , and . Furthermore, for N=2, under the assumptions above, we obtain the boundedness and asymptotic behavior of solutions that provide , , and μ sufficiently large.