%0 Journal Article
%T A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves
%A T. S. Jang
%A Hong Gun Sung
%A Jinsoo Park
%J Mathematical Problems in Engineering
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/472575
%X This paper presents an inverse problem and its solution procedure, which are aimed at identifying a sudden underwater movement of the sea bottom. The identification is mathematically shown to work with a known snapshot data of generated water wave configurations. It is also proved that the problem has a unique solution. However, the inverse problem is involved in an integral equation of the first kind, resulting in an ill-posed problem in the sense of stability. That is, the problem lacks solution stability properties. To overcome the difficulty of solution instability, in this paper, a stabilization technique, called regularization, is incorporated in the present solution procedure for the identification of the sea bottom movement. A numerical experiment is presented to demonstrate that the proposed (numerical) solution procedure operates.
%U http://www.hindawi.com/journals/mpe/2012/472575/