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Dynamics of strongly competing systems with many species


Authors: E. N. Dancer, Kelei Wang and Zhitao Zhang
Journal: Trans. Amer. Math. Soc. 364 (2012), 961-1005
MSC (2010): Primary 35B40, 35R35, 35K57, 92D25
Published electronically: September 15, 2011
MathSciNet review: 2846360
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we prove that the solution of the Lotka-Volterra competing species system with strong competition converges to a stationary point under some natural conditions. We also study the moving boundary problem of the singular limit equation, which plays an important role in our proof.


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Additional Information

E. N. Dancer
Affiliation: School of Mathematics and Statistics, University of Sydney, NSW 2006 Australia
Email: normd@maths.usyd.edu.au

Kelei Wang
Affiliation: Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Address at time of publication: School of Mathematics and Statistics, University of Sydney, NSW 2006 Australia
Email: wangkelei05@mails.gucas.ac.cn, kelei@maths.usyd.edu.au

Zhitao Zhang
Affiliation: Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: zzt@math.ac.cn

DOI: https://doi.org/10.1090/S0002-9947-2011-05488-7
Keywords: Competing species, reaction-diffusion system, free boundary problem
Received by editor(s): April 8, 2010
Received by editor(s) in revised form: September 3, 2010
Published electronically: September 15, 2011
Additional Notes: This work was supported by the Australian Research Council and the National Natural Science Foundation of China (10831005, 10971046)
Article copyright: © Copyright 2011 American Mathematical Society