A Priori Bounds for Elastic Scattering by Deterministic and Random Unbounded Rough Surfaces (CSIAM Transactions on Applied Mathematics, 2023)
This paper investigates the elastic scattering by unbounded deterministicand random rough surfaces, both of which are assumed to be graphs of Lipschitz continuous functions. For the deterministic case, an a priori bound explicitly dependenton frequencies is derived by the variational approach. For the scattering by randomrough surfaces with a random source, well-posedness of the corresponding variationproblem is proved. Moreover, a similar bound with explicit dependence on frequencies for the random case is also established based upon the deterministic result, Pettismeasurability theorem and Bochner’s integrability theorem.