Absence of Blow‐Up in a Fully Parabolic Chemotaxis System With Weakly Singular Sensitivity and Logistic Damping in Dimension Two

ABSTRACT It is shown in this article that blow‐up does not occur in the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain : where , and are positive parameters. Previous results have already established the same conclusion for the parabolic‐elliptic case, where the second equation is replaced by . Here, we complement these findings by extending the result to the fully parabolic case.