Journal article
Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity
Mathematical models & methods in applied sciences, Vol.24(14), pp.2819-2849
12/01/2014
DOI: 10.1142/S0218202514500389
Abstract
Proceeding with a series of works (Refs. 12, 23-25) by the authors, this paper establishes the nonlinear asymptotic stability of traveling wave solutions of the Keller-Segel system with nonzero chemical diffusion and linear consumption rate, where the right asymptotic state of cell density is vacuum (zero) and the initial value is a perturbation with zero integral from the spatially shifted traveling wave. The main challenge of the problem is various singularities caused by the logarithmic sensitivity and the vacuum asymptotic state, which are overcome by a Hopf-Cole type transformation and the weighted energy estimates with an unbounded weight function introduced in the paper.
Details
- Title: Subtitle
- Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity
- Creators
- Jingyu Li - Northeast Normal UniversityTong Li - University of IowaZhi-An Wang - Hong Kong Polytechnic University
- Resource Type
- Journal article
- Publication Details
- Mathematical models & methods in applied sciences, Vol.24(14), pp.2819-2849
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- DOI
- 10.1142/S0218202514500389
- ISSN
- 0218-2025
- eISSN
- 1793-6314
- Number of pages
- 31
- Grant note
- China Postdoctoral Science Foundation 11101073; 11371082 / Chinese NSF 502711 / Hong Kong RGC General Research Fund
- Language
- English
- Date published
- 12/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984240875302771
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