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Traveling bands for the Keller-Segel model with population growth. (English) Zbl 1330.35461

Summary: This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that collective interaction of cell growth and chemical consumption rate plays an essential role in the generation of traveling bands. The research in the paper provides new insights into the mechanisms underlying the chemotactic pattern formation of wave bands.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35C07 Traveling wave solutions
35K55 Nonlinear parabolic equations
46N60 Applications of functional analysis in biology and other sciences
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C17 Cell movement (chemotaxis, etc.)
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References:

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