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Existence and uniqueness of radially symmetric stationary points within the gradient theory of phase transitions
Published online by Cambridge University Press: 26 September 2008
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We study radially symmetric stationary points of the functional
where u denotes the density of a fluid confined to a container Ω, W(u) is the course-grain free energy and ε accounts for surface energy. Under the further assumption of small energy, that is
for small ε, we prove existence of precisely two solutions for the corresponding Euler-Lagrange equation. Each of these solutions is monotone in the radial direction and converges as ε→0 to one of two possible radially symmetric single interface minimizers of E0. Our main tool is the method of matched asymptotic expansions from which we construct exact solutions.
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- Copyright © Cambridge University Press 1995
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