H1-conditional stability with explicit Lipshitz constant for a one-dimensional inverse acoustic problem

2001

Closed access Metadata (CSL-JSON)
DOI 10.1515/jiip.2001.9.3.249
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

Abstract - In the present paper we formulate and investigate a one-dimensional inverse acoustic problem in the form of a nonlinear system of Volterra integral equations. We prove the conditional stability of the inverse problem with explicitly given Lipschitz constant depending only on the depth l and on bounds of the norms of the unknown coefficient and inverse problem data. The proposed technique can be applied to prove the local well-posedness of the inverse problem in L 2(0, l).