A special seminar on “OPTIMAL CONTROL AND FEEDBACK CONTROL PROBLEMS OF INFLUENZA MODELS” by Hee-Dae Kwon, and “MATHEMATICAL ANALYSIS OF BUBBLY MEDIA” by Hyundae Lee from Inha University, Incheon, South Korea. The seminar is scheduled on __January ____13, 2020____ from ____10.00 – 12.00 a.m.____ at M building, venue room __** M307**.

Abstract:

1. “OPTIMAL CONTROL AND FEEDBACK CONTROL PROBLEMS OF INFLUENZA MODELS” by Hee-Dae Kwon

In this talk, we consider various optimal control problems to derive an effective vaccination strategy for influenza outbreaks.

Variations in the SEIAR model are considered to include age structure and control strategies include vaccination, antiviral treatment, and social distancing such as school closures. We investigate an optimal control problem of a SIR reaction-diffusion system. The control problem reflect realistic restrictions associated with limited total vaccination coverage and the maximum daily vaccine administration. A feedback control problem of a SIR model based on the Hamilton-Jacobi-Bellman equation is also considered.

2. “MATHEMATICAL ANALYSIS OF BUBBLY MEDIA” by Hyundae Lee

The study of metamaterials has drawn increasing interest nowadays because of their many important applications in fields such as super-resolution, cloaking, and novel optic and phononic devices.

The bubbly media, because of the simplicity of the acoustic properties of the air bubbles, becomes a natural model for such study.

It is known that a single bubble in the water possesses a quasi-static resonance which is called the Minneart resonance.

Our analysis shows that near and below the Minneart resonant frequency, the effective media has high refractive index, which explains the super-focusing phenomenon observed in the experiment while near and above the Minneart resonant frequency, the effective media is dissipative.

We also present some works on bubbly meta-surface which is a homogenization theory for a thin layer of periodically arranged bubbles mounted on a perfect reflection surface.

Finally, we prove the existence of a subwavelength phononic bandgap in bubble phononic crystals.

The key result is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble.

We also show the existence of a Dirac dispersion cone in a honeycomb crystal comprised of bubbles of arbitrary shape.

It is known that a single bubble in the water possesses a quasi-static resonance which is called the Minneart resonance.

Our analysis shows that near and below the Minneart resonant frequency, the effective media has high refractive index, which explains the super-focusing phenomenon observed in the experiment while near and above the Minneart resonant frequency, the effective media is dissipative.

We also present some works on bubbly meta-surface which is a homogenization theory for a thin layer of periodically arranged bubbles mounted on a perfect reflection surface.

Finally, we prove the existence of a subwavelength phononic bandgap in bubble phononic crystals.

The key result is an original formula for the quasi-periodic Minnaert resonance frequencies of an arbitrarily shaped bubble.

We also show the existence of a Dirac dispersion cone in a honeycomb crystal comprised of bubbles of arbitrary shape.