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OverviewThis book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging. Full Product DetailsAuthor: Mourad ChoulliPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: 1st ed. 2016 Dimensions: Width: 15.50cm , Height: 0.50cm , Length: 23.50cm Weight: 1.533kg ISBN: 9783319336411ISBN 10: 331933641 Pages: 81 Publication Date: 14 June 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsThis book presents, in a unified framework, a thorough treatment of Carleman inequalities, and employs them to investigate the elliptic Cauchy problem and some classical elliptic inverse problems. ... Throughout the book, numerous particular cases and examples are provided to explain the primary results. The book is written in a clear and concise manner ... . (Akhtar A. Khan, Mathematical Reviews, August, 2017) The author provides a unified approach to the study of both elliptic Cauchy problems and some elliptic inverse problems. ... This book is well written and I highly recommend it to those who are interested in inverse problems for partial differential equations. (Dinh Nho Hao, zbMATH, 1351.35260, 2017) The author provides a unified approach to the study of both elliptic Cauchy problems and some elliptic inverse problems. ... This book is well written and I highly recommend it to those who are interested in inverse problems for partial differential equations. (Dinh Nho Hao, zbMATH, 1351.35260, 2017) Author InformationTab Content 6Author Website:Countries AvailableAll regions |