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Global solutions to a chemotaxis system with non-diffusive memory

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
410
Issue
2
Identifiers
DOI: 10.1016/j.jmaa.2013.08.065
Keywords
  • Chemotaxis System
  • Global Solutions
Disciplines
  • Mathematics

Abstract

Abstract In this article, an existence theorem of global solutions with small initial data belonging to L1∩Lp, (n<p⩽∞) for a chemotaxis system is given on the whole space Rn, n⩾3. In the case p=∞, our global solution is integrable with respect to the space variable on some time interval, and then conserves the mass for a short time, at least. The system consists of a chemotaxis equation with a logarithmic term and an ordinary equation without diffusion term.

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