Qualitative Behavior of a Keller-Segel Model with Non-Diffusive Memory

In this paper a one-dimensional Keller-Segel model with a logarithmic chemotactic-sensitiviy and a non-diffusing chemical is classified with respect to its long time behavior. The strength of production of the non-diffusive chemical has a strong influence on the qualitative behavior of the system concerning existence of global solutions or Dirac-mass formation. Further, the initial data play a crucial role