Qualitative behavior of a Keller-Segel model with non-diffusive memory - Kang, Kyungkeun; Stevens, Angela; Velázquez, J. J. L. (Communications in partial differential equations, 2010)
In this paper a one-dimensional Keller-Segel model with a logarithmic chemotactic-sensitivity 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.