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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 16
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Articles

Stabilization in the Keller–Segel system with signal-dependent sensitivity

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Pages 2877-2891 | Received 20 Oct 2018, Accepted 17 Feb 2019, Published online: 01 Mar 2019
 

Abstract

This paper deals with the Keller–Segel system with signal-dependent sensitivity ut=Δuχ(uS(v)v),vt=Δvv+u, where χ>0 and S is a given function generalizing the sensitivity S(s)=1/(a+s)k, k>1, a0, and shows exponential convergence of global classical solutions under an additional smallness condition for χ>0.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

TB and JL acknowledge support of the Deutsche Forschungsgemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. MM is funded by Japan Society for the Promotion of Science (JSPS) Research Fellowships for Young Scientists (No. 17J00101) and JSPS Overseas Challenge Programme for Young Researchers.

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