Free Boundary Problems, System of Equations for Bose–Einstein Condensate and Competing Species

  • Zhitao Zhang
Part of the Developments in Mathematics book series (DEVM, volume 29)


In Chap. 11, we study free boundary problems, Schrödinger systems from Bose–Einstein condensates, and competing systems with many species. We prove the existence and uniqueness result of the Dirichlet boundary value problem of elliptic competing systems. We show that, for the singular limit, species are spatially segregated; they satisfy a remarkable system of differential inequalities as κ→+∞. We also introduce optimal partition problems related to eigenvalues and nonlinear eigenvalues. Finally, some recent new results on Schrödinger systems from Bose–Einstein condensates are presented.


Comparison Principle Free Boundary Problem Einstein Condensate Solitary Wave Solution Singular Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Zhitao Zhang
    • 1
  1. 1.Academy of Mathematics & Systems ScienceThe Chinese Academy of SciencesBeijingP.R. China

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