2024/01/28 by Guanghui Hu, Tianjiao Wang, Hu, Guanghui +5
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #35A15 #35P25 #74J20 #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Geophysical Methods and Applications #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.2401.15581
openalex publication_date 2024/01/28 · openalex created_date 2024/01/31 · openalex updated_date 2026/07/28
In this paper, we investigate well-posedness of time-harmonic scattering of elastic waves by unbounded rigid rough surfaces in three dimensions. The elastic scattering is caused by an L2 function with a compact support in the x3-direction, and both deterministic and random surfaces are investigated via the variational approach. The rough surface in a deterministic setting is assumed to be Lipschitz and lie within a finite distance of a flat plane, and the scattering is caused by an inhomogeneous term in the elastic wave equation whose support lies within some finite distance of the boundary. For the deterministic case, a stability estimate of elastic scattering by rough surface is shown at an arbitrary frequency. It is noticed that all constants in \it a priori bounds are bounded by explicit functions of the frequency and geometry of rough surfaces. Furthermore, based on this explicit dependence on the frequency together with the measurability and ℙ-essentially separability of the randomness, we obtain a similar bound for the solution of the scattering by random surfaces.