T-junction of ferroelectric wires
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 5, pp. 1429-1463.

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.

DOI : 10.1051/m2an/2020001
Classification : 35Q61, 78A25, 49J20
Mots-clés : Electric polarization, nonlocal problems, optimal control, wire, junctions 
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Carbone, Luciano; Gaudiello, Antonio; Hernández-Llanos, Pedro. T-junction of ferroelectric wires. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 5, pp. 1429-1463. doi : 10.1051/m2an/2020001. http://www.numdam.org/articles/10.1051/m2an/2020001/

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