Nonlinear time-harmonic Maxwell equations in an anisotropic medium

来源 :2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal | 被引量 : 0次 | 上传用户：ntfan

【摘要】

：

　　We present recent joint work with J. Mederski (Toru(n)) on the existence of solutions E : Ω→R3 of the problem {▽×(μ(x)-1▽×E)-ω2ε(x)E =(e)EF(x,E) in

【作者】

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Thomas Bartsch

【机构】

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GiessenUniversity,Germany

【出处】

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2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal

【发表日期】

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2016年5期

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　　We present recent joint work with J. Mederski (Toru(n)) on the existence of solutions E : Ω→R3 of the problem {▽×(μ(x)-1▽×E)-ω2ε(x)E =(e)EF(x,E) in Ω v×E = 0 on (e)Ω on a bounded smooth domain Ω (()R3 with exterior normal v : (e)Ω→R3. Here ▽× denotes the curl operator in R3.The equation describes the propagation of the time-harmonic electric field R(E(x)eiwt) in an anisotropic material with a magnetic permeability tensor u(x)∈R3×3 and a permittivity tensor ε(x)∈R3×3, both tensors being symmetric and positive definite. The boundary conditions are those for Ω surrounded by a perfect conductor. The model nonlinearity F : Ω×R3→R is of Kerr-type: F(x,E) = |Γ(x)E|p for some 2 < p < 6 with Γ(x)∈R3×3 invertible.Without symmetry conditions on the material we find ground and bound state solutions.If the material is uniaxial we also find two types of solutions with cylindrical symmetries.

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Nonlinear time-harmonic Maxwell equations in an anisotropic medium

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