2023/02/25 by Tianjiao Wang, Wang, Tianjiao, Xiang Xu +2
Computer Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2302.12996
openalex publication_date 2023/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, which both are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependent on frequencies is derived by the variational approach. For the scattering by random rough surfaces with a random source, well-posedness of the corresponding variation problem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettis measurability theorem and Bochner's integrability Theorem.