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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Dynamics of strongly competing systems with many species
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by E. N. Dancer, Kelei Wang and Zhitao Zhang PDF
Trans. Amer. Math. Soc. 364 (2012), 961-1005 Request permission

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
  • 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)
  • © Copyright 2011 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 961-1005
  • MSC (2010): Primary 35B40, 35R35, 35K57, 92D25
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05488-7
  • MathSciNet review: 2846360