Inverse Problems in Shallow Oceans

9402539吉尔伯特该研究旨在调查浅海中的正声波和逆声波问题。 方法是利用均匀化来推导海底系统的确定性和随机性微分方程。 有几个开放的问题仍然与确定性问题，如正确制定的远场，身份不明的包含问题，并为此事，证明存在的基本奇异解决方案和有效的计算方法找到它。 均匀化方法产生确定性模型作为零阶项，一阶项通过提出随机微分方程来考虑介质的随机性质。 本研究旨在研究这一随机微分方程，并提出和研究与之相关的随机反问题。

9402539 Gilbert The research seeks to investigate direct and inverse acoustic problems in shallow oceans. The approach would be to use homogenization to derive the deterministic and stochastic differential equations for the ocean seabed system. There are several open problems still associated with the deterministic problem such as a correct formulation of the farfield, the unidentified inclusion problem, and for that matter, the proof of the existence of the fundamental singular solution and an efficient computational method for finding it. The homogenization approach produces the deterministic model as the zero order term and the first order takes in the random nature of the media by proposing a stochastic differential equation. The research is aimed at studying this stochastic differential equation and to pose and investigate the random inverse problems associated with it. ***