The monotonicity method for the inverse crack scattering problem. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Daimon, Tomohiro; Furuya, Takashi; Saiin, Ryuji
• Is Part Of: Inverse problems in science and engineering. Volume 28:Issue 11(2020)
• Page Start: 1570
• Page End: 1581
• Publication Date: 2020-11-01
• Subjects: Inverse scattering -- monotonicity method -- crack detection -- far field operator -- Helmholz equation; 35R30; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2020.1733998
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : The monotonicity method for the inverse acoustic scattering problem is to understand the inclusion relation between an unknown object and artificial one by comparing the far field operator with the artificial operator. This paper introduces the development of this method to the inverse crack scattering problem. Our aim is to give the following two indicators: One (Theorem 1.1) is to determine whether an artificial small arc is contained in the unknown arc. The other one (Theorem 1.2) is whether an artificial large domain contains the unknown one. Finally, numerical examples based on Theorem 1.1 are given.