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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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Concentrating patterns of reaction-diffusion systems: A variational approach
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by Yanheng Ding and Tian Xu PDF
Trans. Amer. Math. Soc. 369 (2017), 97-138 Request permission

Abstract:

Our purpose is to motivate an analytic characterization aimed at predicting patterns for general reaction-diffusion systems, depending on the spatial distribution involved in the reaction terms. It is shown that there must be a pattern concentrating around the local minimum of the chemical potential distribution for small diffusion coefficients. A multiple concentrating result is also established to illustrate the mechanisms leading to emergent spatial patterns. The results of this paper were proved by using a general variational technique. This enables us to consider nonlinearities which grow either super quadratic or asymptotic quadratic at infinity.
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Additional Information
  • Yanheng Ding
  • Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China
  • MR Author ID: 255943
  • Tian Xu
  • Affiliation: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China
  • Address at time of publication: Center for Applied Mathematics, Tianjin University, 300072 Tianjin, People’s Republic of China
  • MR Author ID: 1032453
  • Email: xutian@amss.ac.cn
  • Received by editor(s): April 29, 2014
  • Received by editor(s) in revised form: December 5, 2014
  • Published electronically: March 1, 2016
  • Additional Notes: The second author is the corresponding author

  • Dedicated: Dedicated to Antonio Ambrosetti on the occasion of his 70th birthday
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 97-138
  • MSC (2010): Primary 35A15, 35K57, 49J35
  • DOI: https://doi.org/10.1090/tran/6626
  • MathSciNet review: 3557769