Nonlinear time-harmonic Maxwell equations in domains

@article{Bartsch2016NonlinearTM,
  title={Nonlinear time-harmonic Maxwell equations in domains},
  author={T. Bartsch and Jaroslaw Mederski},
  journal={Journal of Fixed Point Theory and Applications},
  year={2016},
  volume={19},
  pages={959-986}
}
  • T. Bartsch, Jaroslaw Mederski
  • Published 2016
  • Physics, Mathematics
  • Journal of Fixed Point Theory and Applications
  • The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of charges and currents leads to the elliptic equation $$\begin{aligned} \nabla \times \left( \mu (x)^{-1}\nabla \times u\right) - \omega ^2\varepsilon (x)u = f(x,u) \end{aligned}$$∇×μ(x)-1∇×u-ω2ε(x)u=f(x,u)for the field $$u:\Omega \rightarrow \mathbb {R}^3$$u:Ω→R3 in a domain $$\Omega \subset \mathbb {R}^3$$Ω⊂R3. Here, $$\varepsilon (x) \in \mathbb {R}^{3\times 3}$$ε(x)∈R3×3 is the (linear) permittivity tensor… CONTINUE READING
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