@Article{CSIAM-AM-4-4, author = {Wang, Tianjiao and Yiwen, Lin and Xu, Xiang}, title = {A Priori Bounds for Elastic Scattering by Deterministic and Random Unbounded Rough Surfaces}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2023}, volume = {4}, number = {4}, pages = {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.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2023-0001}, url = {https://global-sci.com/article/82303/a-priori-bounds-for-elastic-scattering-by-deterministic-and-random-unbounded-rough-surfaces} }