# Analysis Seminar

#### On the Helmholtz Equations with Sign Changing Coefficients

**Speaker:**
Hoai-Minh Nguyen, EPFL

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, October 15, 2015, 11 a.m.

**Synopsis:**

This talk is devoted to various properties and applications of the Helmholtz equations with sign changing coefficients. These equations are used to model negative index materials which are artificial structures whose refractive index are negative over some frequency range. These materials were first investigated theoretically by Veselago in 1964 and their existence was confirmed experimentally by Shelby et al. in 2001. The study of these equations faces two difficulties. First the ellipticity and the compactness are lost in general due to the changing sign coefficients. Second, the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others as the loss (the viscosity) goes to 0, might occur. In this talk, I will present several remarkable properties of these equations and their applications such as cloaking and superlensing using complementary media and cloaking a source and an object via anomalous localized resonance. Various conditions under which the equations are stable are also mentioned.