A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves. (12th January 2012)

• Record Type: Journal Article
• Authors: Jang, T. S.; Sung, Hong Gun; Park, Jinsoo
• Other Names: Younis Mohammad Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-01-12
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/472575
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.