Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 159, Issue -, Pages 424-457Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2017.02.026
Keywords
Cross-diffusion system; Spiky steady states; Spectral analysis
Categories
Funding
- NSFC [11471221, 11226178, 11501031]
- Beijing Municipal Education Commission [KZ201310028030]
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This paper is concerned with the stability/instability of a type of positive spiky steady states for a quasi-linear cross-diffusion system describing two species competition. By detailed spectral analysis, it is proved that the spiky steady states for the related shadow system are linearly unstable when the diffusion rate is small enough and the positive spiky steady states for the original cross-diffusion system are unstable when the cross diffusion rate for one species is large enough and the diffusion rate of another species is small. (C) 2017 Elsevier Ltd. All rights reserved.
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