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

Kyungkeun Kang; Angela Stevens; Juan J.L. Velázquez

doi:10.1080/03605300903473400

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

Kyungkeun Kang, Angela Stevens, Juan J.L. Velázquez

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Pages (from-to)	245-274
Number of pages	30
Journal	Communications in Partial Differential Equations
Volume	35
Issue number	2
DOIs	https://doi.org/10.1080/03605300903473400
Publication status	Published - 2010 Feb

Bibliographical note

Funding 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

Analysis
Applied Mathematics

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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.",

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

Abstract

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