A high-contrast composite with annular inclusions: Norm-resolvent asymptotics

Using the approach proposed by Cherednichenko, Ershova, and Kiselev in ``Effective Behaviour of Critical-Contrast PDEs: Micro-resonances, Frequency Conversion, and Time Dispersive Properties. I'' (2020). Communications in Mathematical Physics volume 375(3), pages 1833-1884, we investigate the operator-norm resolvent asymptotics of a high-contrast composite, consisting of a ``stiff'' material, with annular ``soft'' inclusions (a ``stiff-soft-stiff'' setup). This setup is derived from two models with very different effective wave propagation behaviors. Then, as a first step towards studying wave propagation on the stiff-soft-stiff composite, we use the effective description to derive analogous ``dispersion functions''.