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T-junction of ferroelectric wires. (English) Zbl 1450.35246

The authors analyze two T-joined ferroelectric wires in 3D, modeled by two joined orthogonal paralellpipeds. There are two non-convex and non-local energy functionals associated to the problem. The asymptotic behavior of limiting problems is considered. All the limit problems considered by the authors remain non-convex, but the non-local behavior disappears in the limit. Depending on what boundary conditions are imposed, it is shown that the limiting behavior of the polarization field can vary.

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory (general)
49J20 Existence theories for optimal control problems involving partial differential equations
49S05 Variational principles of physics
78M50 Optimization problems in optics and electromagnetic theory
78M30 Variational methods applied to problems in optics and electromagnetic theory
78M35 Asymptotic analysis in optics and electromagnetic theory
35B40 Asymptotic behavior of solutions to PDEs
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