The time‐domain scattering by the elastic shell in a two‐layered unbounded structure - Zhang, Lei (Mathematical methods in the applied sciences, 2023)
The subject of this research is the time‐domain scattering problem for a three‐dimensional layered elastic shell submerged in a two‐layered fluid separated by an unbounded rough surface. The essence of the problem is to model the scattering interaction between the given elastic shell and some incident wave in a two‐layered medium. Using the exact transparent boundary condition (TBC), we reformulate the unbounded scattering problem into an equivalent initial‐boundary value problem. The well‐posedness is proved for the problem by the Laplace transform and variational method in the s‐domain. Moreover, we show that the reduced problem has a unique weak solution by the energy method. The priori estimates with explicit dependence on the time are derived for the acoustic pressure and the elastic displacement in the time domain.