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Cet ouvrage est consacré à une introduction aux problèmes inverses elliptiques et paraboliques. L' objectif est de présenter quelques méthodes récentes pour établir des résultats d'unicité et de stabilité. Seront traités quelques problèmes inverses elliptiques devenus maintenant classiques, tels que la conductivité inverse, la détection de corrosion ou de fissures et les problèmes spectraux inverses. Parmi les problèmes inverses paraboliques considérés figurent le problème classique de retrouver une distribution initiale de la chaleur et la localisation de sources, de chaleur ou de pollution par exemple. Les problèmes d'identification de non linéarités seront aussi étudiés.
Cet ouvrage s'adresse à tous ceux qui souhaitent s' intéresser à l'analyse mathématique des problèmes inverses.
This book is devoted to an introduction of elliptic and parabolic inverse problems. Our goal is to present some recent methods for establishing uniqueness and stability results. We study some classical elliptic inverse problems: inverse conductivity problem, detection of corrosion or cracks and inverse spectral problems. Among the parabolic inverse problems we consider the classic problem of finding an initial distribution of heat and the location of sources. We hope that this book will interest all those who want to learn the mathematical analysis of inverse problems.
Cet ouvrage s'adresse à tous ceux qui souhaitent s' intéresser à l'analyse mathématique des problèmes inverses.
This book is devoted to an introduction of elliptic and parabolic inverse problems. Our goal is to present some recent methods for establishing uniqueness and stability results. We study some classical elliptic inverse problems: inverse conductivity problem, detection of corrosion or cracks and inverse spectral problems. Among the parabolic inverse problems we consider the classic problem of finding an initial distribution of heat and the location of sources. We hope that this book will interest all those who want to learn the mathematical analysis of inverse problems.
From the reviews:
"This is a nicely written monograph which presents a number of basic results about uniqueness and stability for elliptic and parabolic inverse problems in a thorough and uniform manner, and should be of wide interest to researchers in inverse problems for partial differential equations. ... The text concludes with a collection of advanced exercises and a brief discussion of some open problems." (Paul E. Sacks, Mathematical Reviews, Issue 2010 m)
"The book is devoted to the determination of unknown coefficients or unknown - i.e. unaccessible - subdomains or parts of the boundary related to both elliptic and parabolic equations. ... In conclusion, the reviewer not only recommends this well-written book as a good trainer for young mathematicians wishing to be acquainted with inverse problems for PDEs, but also recommends it to researchers, since they can find in it a lot of stimulating ideas and indispensable techniques needed to solve nowadays inverse problems." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1192, 2010)
"This is a nicely written monograph which presents a number of basic results about uniqueness and stability for elliptic and parabolic inverse problems in a thorough and uniform manner, and should be of wide interest to researchers in inverse problems for partial differential equations. ... The text concludes with a collection of advanced exercises and a brief discussion of some open problems." (Paul E. Sacks, Mathematical Reviews, Issue 2010 m)
"The book is devoted to the determination of unknown coefficients or unknown - i.e. unaccessible - subdomains or parts of the boundary related to both elliptic and parabolic equations. ... In conclusion, the reviewer not only recommends this well-written book as a good trainer for young mathematicians wishing to be acquainted with inverse problems for PDEs, but also recommends it to researchers, since they can find in it a lot of stimulating ideas and indispensable techniques needed to solve nowadays inverse problems." (Alfredo Lorenzi, Zentralblatt MATH, Vol. 1192, 2010)