Neutral Inclusions, Weakly Neutral Inclusions, and an Over-Determined Problem for Confocal Ellipsoids

Abstract

An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field, it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such inclusions are of interest in relation to invisibility cloaking and effective medium theory. There have been some attempts lately to construct or to show existence of such inclusions in the form of core-shell structure or a single inclusion with the imperfect bonding parameter attached to its boundary. In this talk, the speaker will review recent progress in such attempts. He will also discuss the over-determined problem for confocal ellipsoids which is closely related with the neutral inclusion, and its equivalent formulation in terms of Newtonian potentials.

About the Speaker

Prof. Hyeonbae KANG received his BS and MS in Mathematics from Seoul National University in 1982 and 1984 respectively. He then obtained his PhD from the University of Wisconsin-Madison in 1989 and continued his research as a Visiting Assistant Professor at the University of Minnesota. He returned to Korea in 1991 and was on the faculty at Soongsil University in 1991-1994, at Korea University in 1994-1997 and at his alma mater, Seoul National University in 1997-2008. He moved to Inha University in 2008 and is currently the Jungseok Chair Professor at the Department of Mathematics there.

Prof. Kang’s research focuses on mathematical problems arising from various area of applications such as inverse problems and imaging, non-destructive evaluation, and continuum mechanics. He is now serving as a Section Editor at the journal, Partial Differential Equations and Applications.

Prof. Kang was awarded the Korean Science Award by the Korean Ministry of Education, Science and Technology and the National Research Foundation of Korea in 2010. He is also the recipient of the 2011 Inchon Award from the Inchon Foundation, the 2015 Kyung-Ahm Prize from the Kyung-Ahm Education & Cultural Foundation and the 2015 KSIAM-Kumkok Award from the Korean Society for Industrial and Applied Mathematics.

For Attendees' Attention

This talk will be held online via Zoom. To attend, please join the Zoom meeting at https://hkust.zoom.us/j/99292085086 (Meeting ID: 992 9208 5086 / Passcode: iasip2022).

About the Program

For more information, please refer to the program website at https://iasprogram.hkust.edu.hk/inverseproblems/.