Approximate acoustic cloaking in inhomogeneous isotropic space

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• 作者：JingZhi Li (1)
  HongYu Liu (2)
  ShiPeng Mao (3)
  
• 关键词：transformation optics ; approximate invisibility cloaking ; scattering estimates ; integral operator equations ; 35Q60 ; 35R30 ; 78A46 ; 46N20
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2013
• 出版时间：December 2013
• 年：2013
• 卷：56
• 期：12
• 页码：2631-2644
• 全文大小：
• 作者单位：JingZhi Li (1)
  HongYu Liu (2)
  ShiPeng Mao (3)
  
  1. Faculty of Science, South University of Science and Technology of China, Shenzhen, 518055, China
  2. Department of Mathematics and Statistics, University of North Carolina, Charlotte, NC, 28223, USA
  3. LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
  
• ISSN：1869-1862

文摘

We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the “blow-up-a-small-region” construction. This is based on novel scattering estimates corresponding to multiple multi-scale obstacles located in an isotropic space. We develop a novel system of integral equations to decouple the nonlinear scattering interaction among the small obstacle components, the regular obstacle components and the inhomogeneous background medium.