| Issue |
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
|
|
|---|---|---|
| Page(s) | 1429 - 1463 | |
| DOI | https://doi.org/10.1051/m2an/2020001 | |
| Published online | 26 June 2020 | |
T-junction of ferroelectric wires
1
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
2
Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile
* Corresponding author: gaudiell@unina.it
Received:
2
December
2019
Accepted:
23
December
2019
In this paper, starting from a non-convex and nonlocal 3D variational mathematical model for the electric polarization in a ferroelectric material, and using an asymptotic process based on dimensional reduction, we analyze junction phenomena for two orthogonal joined ferroelectric wires. Depending on the initial boundary conditions, we get several different limit problems, sometimes uncoupled. We point out that all the limit problems remain non-convex, but the nonlocality disappears.
Mathematics Subject Classification: 35Q61 / 78A25 / 49J20
Key words: Electric polarization / nonlocal problems / optimal control / wire / junctions
© EDP Sciences, SMAI 2020
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