| The study of invisibility and visibility of elastic waves is of great significance for the understanding and application of the fields of acoustics,elasticity and seismology.Invisibility and visibility of elastic waves can be applied to problems of sound isolation and noise control.At the same time,invisibility and visibility of elastic waves can be applied to related problems such as simulation of seismic wave propagation.Therefore,explore the mathematics of invisibility and visibility of elastic waves The derivation and proof of model and related formula are the important basis for exploring these application fields.More importantly,studying the invisibility and visibility of elastic waves also contributes to the development of new materials to improve and optimize existing engineering and scientific applications For example,in materials science,studying the invisibility and visibility of elastic waves can be used to design novel vibration isolation materials and acoustic materials.Finally,Studying mathematical models of invisibility and visibility of elastic waves,also helps to improve our understanding of nature and physical phenomena.Studying invisibility and visibility of elastic waves can be used to explore the structure of the Earth’s interior.In addition,understanding mathematical properties of invisibility and visibility of elastic waves can also help to discover new physical laws and theories.In this paper,we consider scattering problems related to elastic waves.We prove that for elastic scatterers with corners,invisibility cannot occur at the corners and scattering must be visible.To demonstrate this conclusion,we study the geometric structure of two-dimensional elastic scatterers at corners when invisibility occurs.Using complex geometric optics solutions,we study elastic scatterers with corners under different regularity conditions of the wave field,and we demonstrate that scattering must occur at the corners.Specifically,we analyze complex geometric optics solutions using integral equation methods and harmonic analysis.In recent years,the issues of invisibility and visibility have received widespread attention and development,which is of great significance for our study of visibility and invisibility in elastic wave scattering problems. |
