Communications in Mathematical Sciences

Volume 16 (2018)

Number 3

The direct and inverse elastic scattering problems for two scatterers in contact

Pages: 857 – 877

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n3.a12

Authors

Jun Guo (School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan, China)

Hao Wu (School of Mathematics and Statistics, South-Central University For Nationalities, Wuhan, China)

Lei Xiao (School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, China)

Abstract

This paper is concerned with the elastic scattering problem of a combined scatterer, which consists of a penetrable obstacle and a hard crack touching with each other. By using the boundary integral equation method, the direct scattering problem is formulated as a boundary integral system, then we obtain the existence and uniqueness of a weak solution according to Fredholm theory. The inverse scattering problem we are dealing with is the shape reconstruction of the combined scatterer from the knowledge of far field patterns due to the incident plane compressional and shear waves. Based on an analysis of a particular transmission eigenvalue problem, the linear sampling method is established to reconstruct the combined scatterer. The numerical experiments show the feasibility and validity of the proposed method.

Keywords

elastic scattering, combined scatterer, linear sampling method

2010 Mathematics Subject Classification

35Q30, 35R30

Full Text (PDF format)

This research is supported by National Natural Science Foundation of People’s Republic of China, No. 11571132, and the Fundamental Research Funds for South-Central University for Nationalities, No. CZT18010.

Received 24 September 2017

Received revised 26 February 2018

Accepted 26 February 2018

Published 30 August 2018