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.
Bibliographical noteFunding Information:
This paper was done while all three authors were at the Max-Planck-Institute for Mathematics in the Sciences, in Leipzig, Germany. Additionally Kang was partially supported by KRF-2008-331-C00024 and R01-2008-000-11008-0. J.J.L. Velázquez was also supported by the Humboldt foundation and by DGES Grant MTM2007-61755. Further support was given by The International Graduate College IGK 710, Heidelberg, funded by the Deutsche Forschungsgemeinschaft, (DFG).
All Science Journal Classification (ASJC) codes
- Applied Mathematics