The time‐domain scattering by the elastic shell in a two‐layered unbounded structure

• Published in: Mathematical methods in the applied sciences Vol. 46; no. 5; pp. 5696 - 5724
• Main Author: Zhang, Lei
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.03.2023
• Subjects: Boundary conditions; Boundary value problems; elastic shell scattering; Elastic shells; Energy methods; Incident waves; Navier equation; transparent boundary condition; unbounded rough surface; variational method; wave equation
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.8863

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.