Chemotactic traveling waves with compact support

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A logarithmic model type chemotaxis equation is introduced with porous medium diffusion and a population dependent consumption rate. The classical assumption that individual bacterium can sense the chemical gradient is not taken. Instead, the chemotactic term appears by assuming that the migration distance is inversely proportional to the amount of food if food is the reason for migration. The existence and uniqueness of a traveling wave solution of the model are obtained. In particular, solutions have interfaces that divide into constant and non-constant regions. In particular, the profile of the population distribution has compact support. Numerical simulations are provided and compared with analytic results.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2020-08
Language
English
Article Type
Article
Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.488, no.2

ISSN
0022-247X
DOI
10.1016/j.jmaa.2020.124090
URI
http://hdl.handle.net/10203/274129
Appears in Collection
MA-Journal Papers(저널논문)
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