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

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Book cover Variational, Topological, and Partial Order Methods with Their Applications

Part of the book series: Developments in Mathematics ((DEVM,volume 29))

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Abstract

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.

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Authors and Affiliations

  1. Academy of Mathematics & Systems Science, The Chinese Academy of Sciences, Beijing, P.R. China

    Zhitao Zhang

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  1. Zhitao Zhang
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Zhang, Z. (2013). Free Boundary Problems, System of Equations for Bose–Einstein Condensate and Competing Species. In: Variational, Topological, and Partial Order Methods with Their Applications. Developments in Mathematics, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30709-6_11

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