| Abstract: |
| We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity is first removed via the inverse Hopf-Cole transformation, then, for the transformed system, we study the Green`s function of the corresponding linear system, linearized around a constant equilibrium solution , and the results give us a detailed point-wise description of the Green`s function. Next, with the results on Green`s function, we study small data solution to the nonlinear system by making use of Duhamel`s principle. This provides a descriptive asymptotic behavior in a point-wise sense, which also leads to $L^1$-asymptotic behavior. |
|