Abstract
In this chapter we establish the limit equations of the singularly perturbed elliptic and parabolic systems arising in the study of Bose–Einstein condensation. The proof relies on a stationary condition and a monotonicity formula.
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Notes
- 1.
In [21], we exclude the possibility to have one component of u, say u 1, vanishing on a locally smooth hypersurface, where u 1 is strictly positive in a deleted neighborhood of this hypersurface, so called multiplicity 1 points on the free boundary. This result is essential to prove that (7.3) is the limit of (7.1).
- 2.
For a proof, see [20].
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Wang, K. (2013). The Limit Equation of a Singularly Perturbed System. In: Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33696-6_7
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DOI: https://doi.org/10.1007/978-3-642-33696-6_7
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