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plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle\u2019s shape and the impedances (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03bc<\/mml:mi><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03bb<\/mml:mi><\/mml:mrow><\/mml:math>) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method.<\/jats:p>","DOI":"10.1155\/2015\/195460","type":"journal-article","created":{"date-parts":[[2015,9,28]],"date-time":"2015-09-28T21:01:44Z","timestamp":1443474104000},"page":"1-13","source":"Crossref","is-referenced-by-count":5,"title":["Multilayered Scattering Problem with Generalized Impedance Boundary Condition on the Core"],"prefix":"10.1155","volume":"2015","author":[{"given":"Jun","family":"Guo","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, China"}]},{"given":"Guozheng","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China"}]},{"given":"Mingjian","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, South-Central University for Nationalities, 182 Minyuan Road, Wuhan 430074, China"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-37689-5"},{"key":"3","year":"1998"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1137\/130921350"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1093\/qjmam\/27.1.129"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1137\/090777578"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/26\/1\/015002"},{"issue":"7","key":"9","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1002\/(SICI)1099-1476(19980510)21:7<619::AID-MMA940>3.0.CO;2-P","volume":"21","year":"1998","journal-title":"Mathematical Methods in the Applied Sciences"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1137\/s0036141097318614"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2007.06.020"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1137\/110850347"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/12\/4\/003"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/19\/6\/057"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144500367337"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/17476933.2011.625089"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/1\/023"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/29\/4\/045009"},{"key":"21","series-title":"edited by: R. 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