为了找到最简单和最有效的形状的噪声吸收壁耗散声波的声能，我们考虑的频率模型描述的亥姆霍兹方程的边界上的阻尼。模型的适定性在一类具有d-集边界（N - 1 $\le$ d < N）的域中得到证明.我们引入一类容许Lipschitz边界，其中存在一个最佳形状的壁在以下意义上：我们证明了存在一个Radon措施在这个形状上，大于或等于通常的勒贝格测度，相应的解决方案的亥姆霍兹问题实现的下确界的声能定义的勒贝格测度的边界上。如果这个Radon测度与勒贝格测度一致，则相应的解实现了能量的最小值。对于一个固定的多孔材料，被认为是一种声吸收剂，我们推导出相应的阻尼波动方程（阻尼体积）描述的时间相关的问题，其边界的阻尼参数。
英文摘要：
In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The well-posedness of the model is shown in a class of domains with d-set boundaries (N -- 1 $\le$ d < N). We introduce a class of admissible Lipschitz boundaries, in which an optimal shape of the wall exists in the following sense: We prove the existence of a Radon measure on this shape, greater than or equal to the usual Lebesgue measure, for which the corresponding solution of the Helmholtz problem realizes the infimum of the acoustic energy defined with the Lebesgue measure on the boundary. If this Radon measure coincides with the Lebesgue measure, the corresponding solution realizes the minimum of the energy. For a fixed porous material, considered as an acoustic absorbent, we derive the damping parameters of its boundary from the corresponding time-dependent problem described by the damped wave equation (damping in volume).
Wave propagation in the frequency regime in one-dimensional quasiperiodic media -Limiting absorption principle
Columbia University（哥伦比亚大学）；APAM, Columbia University, United States（美国哥伦比亚大学应用物理与应用数学系）；POEMS, CNRS, Inria, ENSTA, Institut Polytechnique de Paris,91120 Palaiseau, France（法国帕莱索欧洲光学与测量工程实验室（POEMS），法国国家科学研究中心（CNRS），法国国家信息与自动化研究所（Inria），国立高等先进技术学院（ENSTA），巴黎理工学院）
