Asymptotic behavior of spectral of Neumann‐Poincaré operator in Helmholtz system. (28th November 2018)

• Record Type: Journal Article
• Authors: Fang, Xiaoping; Deng, Youjun; Chen, Xiaohong
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 3(2019)
• Page Start: 942
• Page End: 953
• Publication Date: 2018-11-28
• Subjects: asymptotic behavior -- Helmholtz system -- Neumann‐Poincaré operator -- spectral analysis; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5397
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we are concerned with the asymptotic behavior of the Neumann‐Poincaré operator in Helmholtz system. By analyzing the asymptotic behavior of spherical Bessel function near the origin and/or approach higher order, we prove the asymptotic behavior of spectral of Neumann‐Poincaré operator when frequency is small enough and/or the order is large enough. The results show that spectral of Neumann‐Poincaré operator is continuous at the origin and converges to 0 from the complex plane in general.