CSIAM Trans. Appl. Math., 4 (2023), pp. 696-720.
Published online: 2023-10
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This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, both of which 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.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2023-0001}, url = {http://global-sci.org/intro/article_detail/csiam-am/22075.html} }This paper investigates the elastic scattering by unbounded deterministic and random rough surfaces, both of which 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.