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Time-harmonic and asymptotically linear Maxwell equations in anisotropic media
- Source :
- Mathematical Methods in the Applied Sciences. 41:317-335
- Publication Year :
- 2017
- Publisher :
- Wiley, 2017.
-
Abstract
- This paper is focused on following time-harmonic Maxwell equation: ∇×(μ−1(x)∇×u)−ω2e(x)u=f(x,u),inΩ,ν×u=0,on∂Ω, where Ω⊂R3 is a bounded Lipschitz domain, ν:∂Ω→R3 is the exterior normal, and ω is the frequency. The boundary condition holds when Ω is surrounded by a perfect conductor. Assuming that f is asymptotically linear as |u|→∞, we study the above equation by improving the generalized Nehari manifold method. For an anisotropic material with magnetic permeability tensor μ∈R3×3 and permittivity tensor e∈R3×3, ground state solutions are established in this paper. Applying the principle of symmetric criticality, we find 2 types of solutions with cylindrical symmetries in particular for the uniaxial material.
- Subjects :
- General Mathematics
010102 general mathematics
Mathematical analysis
General Engineering
01 natural sciences
010101 applied mathematics
symbols.namesake
Lipschitz domain
Maxwell's equations
Bounded function
Homogeneous space
symbols
Tensor
Boundary value problem
0101 mathematics
Perfect conductor
Nehari manifold
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........29bd26f0d2f3dbf09db77ef671bad6a7