Semiclassical states for the curl-curl problem

2023/12/06 by Bieganowski, Bartosz, Konysz, Adam, Mederski, Jarosław
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.03658

Abstract

We show the existence of the so-called semiclassical states U:ℝ³→ℝ³ to the following curl-curl problem ε² ∇ × (∇ × U) + V(x) U = g(U), for sufficiently small ε > 0. We study the asymptotic behaviour of solutions as ε→ 0⁺ and we investigate also a related nonlinear Schrödinger equation involving a singular potential. The problem models large permeability nonlinear materials satisfying the system of Maxwell equations.

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