Une introduction aux problmes inverses elliptiques et paraboliques [Paperback]

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 est consacr? ? une introduction aux probl?mes inverses elliptiques et paraboliques. L objectif est de pr?senter quelques m?thodes r?centes pour ?tablir des r?sultats dunicit? et de stabilit?. Seront trait?s quelques probl?mes inverses elliptiques devenus maintenant classiques, tels que la conductivit? inverse, la d?tection de corrosion ou de fissures et les probl?mes spectraux inverses. Parmi les probl?mes inverses paraboliques consid?r?s figurent le probl?me classique de retrouver une distribution initiale de la chaleur et la localisation de sources, de chaleur ou de pollution par exemple. Les probl?mes didentification de non lin?arit?s seront aussi ?tudi?s.

Cet ouvrage sadresse ? tous ceux qui souhaitent s int?resser ? lanalyse math?matique des probl?mes 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 inversel$