Year: 2023
Author: Tianjiao Wang, Yiwen Lin, Xiang Xu
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 696–720
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.SO-2023-0001
CSIAM Transactions on Applied Mathematics, Vol. 4 (2023), Iss. 4 : pp. 696–720
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Elastic wave scattering unbounded rough surface variation problem a priori bound.