2025/11/07 by He, Youzi, Wu, Wei, Dang, Hongyi
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2511.04999
openalex publication_date 2025/11/07 · openalex created_date 2025/11/11 · openalex updated_date 2026/07/28
This paper establishes uniqueness results of inverse elastic scattering problem with phaseless near-field data in periodic structures in ℝ2 and periodic/biperiodic structures in ℝ3. We use a superposition of two point sources in each periodic unit with different positions as the incident field, and measures the phaseless near-field data on a line parallel to x1-axis in 2D, or on a plane parallel to (x1,x2)-plane in 3D. We first calculate the explicit formula of quasi-periodic/biperiodic Green's functions of Lamé system in ℝ3. Then, to establish the uniqueness results, the reciprocity relations for point sources, scattered fields, and total fields are derived. Finally, with the help of Rayleigh's expansion, the uniqueness results are proved. The quasi-periodic/biperiodic Green's functions of Lamé system in ℝ3, the reciprocity relations, and Rayleigh's expansion in ℝ3 are novel results as important by-products in the proof process.