Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations

  • Kelei¬†Wang

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Kelei Wang
    Pages 1-15
  3. Kelei Wang
    Pages 27-44
  4. Kelei Wang
    Pages 61-80
  5. Kelei Wang
    Pages 81-93
  6. Back Matter
    Pages 107-109

About this book


In Bose-Einstein condensates from physics and competing species system from population dynamics, it is observed that different condensates (or species) tend to be separated. This is known as the phase separation phenomena. These pose a new class of free boundary problems of nonlinear partial differential equations. Besides its great difficulty in mathematics, the study of this problem will help us get a better understanding of the phase separation phenomena. This thesis is devoted to the study of the asymptotic behavior of singularly perturbed partial differential equations and some related free boundary problems arising from Bose-Einstein condensation theory and competing species model. We study the free boundary problems in the singular limit and give some characterizations, and use this to study the dynamical behavior of competing species when the competition is strong. These results have many applications in physics and biology.


It was nominated by the Graduate University of Chinese Academy of Sciences as an outstanding PhD thesis.


Bose-Einstein condensate Competition system Free boundary problems Phase separation

Authors and affiliations

  • Kelei¬†Wang
    • 1
  1. 1.Wuhan Inst. of Physics and MathematicsWuhanChina, People's Republic

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-33695-9
  • Online ISBN 978-3-642-33696-6
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site