TY - JOUR
T1 - A Priori Bounds for Elastic Scattering by Deterministic and Random Unbounded Rough Surfaces
AU - Wang , Tianjiao
AU - Lin , Yiwen
AU - Xu , Xiang
JO - CSIAM Transactions on Applied Mathematics
VL - 4
SP - 696
EP - 720
PY - 2023
DA - 2023/10
SN - 4
DO - http://doi.org/10.4208/csiam-am.SO-2023-0001
UR - https://global-sci.org/intro/article_detail/csiam-am/22075.html
KW - Elastic wave scattering, unbounded rough surface, variation problem, a priori bound.
AB - <p style="text-align: justify;">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.</p>