论文标题
确定性和随机周期性结构中Helmholtz方程的稳定性
Stability for the Helmholtz equation in deterministic and random periodic structures
论文作者
论文摘要
在本文中证明了确定性和随机周期结构中Helmholtz方程的稳定性结果。在假设排除共振的假设下，通过在能量空间中的变异方法和傅立叶分析，确定了确定性周期性结构中Helmholtz方程的稳定性估计值。对于随机情况，通过引入可变变换，在随机介质的确定域中，随机结构域中散射问题的变异公式降低了。 PETTIS可测量定理和Bochner定理结合了灭绝症情况的稳定性结果，并通过随机周期性结构来实现散射问题的稳定性，并得出了稳定性。两种稳定性估计都相对于波数明确。
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deteministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber.
