A Mathematical Theory of Subwavelength Resonances in Elasticity with Applications and Beyond

In this project, we aim to establish a comprehensive mathematical theory of the subwavelength resonances in linear elasticity. By the subwavelength scale, we mean the size of the material device is smaller than the operating wavelength. Based on the obtained resonance results, we consider their applications to the studies of several cutting-edge applications including the effective constructions of elastic metamaterials, super-resolution elastic wave imaging and guiding elastic wave propagations. Moreover, two completely new and highly intriguing spectral problems arise from the above proposed studies. We shall also conduct a systematic study and achieve a thorough understanding of these spectral problems. Then we shall consider the applications of the obtained spectral results to tackle several challenging inverse problems and elastic wave imaging problems of practical significances that go beyond the subwavelength regime.