Cloking Due To Anomalous Localized Resonance In R~3

This work concerns the cloaking due to anomalous localized resonance(CALR) in the quasi-static regime. We extend the related two-dimensional studies to the threedimensional setting. CALR is shown not to take place for the plasmonic configuration considered in two papers in the three-dimensional case. We give two different constructions which ensure the occurrence of CALR that are proved based on variational principle and Fourier series.The contents of the thesis are as follows:In Chapter 1, we introduce the research background and the research status of the cloaking due to anomalous localized resoance and some basic knowledge including the principle and the structure of the cloaking.In Chapter 2, by using the primary variational principle and dual variational principle argument, we show the nonoccurrence and occurrence of CALR by taking the loss parameter to be given over the whole space R3.In Chapter 3, we consider the occurrence and nonoccurrence of CALR by taking the loss parameter to be given only in the plasmonic layer and the relevant proof is based on the Fourier series.In the last Chapter, a summary of this thesis is presented and some interesting unsolved problems are addressed.