Qualitative behavior of a Keller-Segel model with non-diffusive memory

Kyungkeun Kang, Angela Stevens, and Juan J.L. Velazquez

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Submission date: 21. Apr. 2008
Pages: 30
published in: Communications in partial differential equations, 35 (2010) 2, p. 245-274 
DOI number (of the published article): 10.1080/03605300903473400
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Abstract:
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.