Une introduction aux problm̈es inverses elliptiques et paraboliques

• Main Author: Choulli, Mourad. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: French
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Mathm̌atiques et Applications, 65
• Subjects: Mathematics.; Differential equations, partial.; Partial Differential Equations.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-02460-3

 Cet ouvrage est consacr ̌ ̉une introduction aux problm̈es inverses elliptiques et paraboliques. L<U+0019> objectif est de pršenter quelques mťhodes rčentes pour ťablir des ršultats d<U+0019>unicit ̌et de stabilit.̌ Seront traitš quelques problm̈es inverses elliptiques devenus maintenant classiques, tels que la conductivit ̌inverse, la dťection de corrosion ou de fissures et les problm̈es spectraux inverses. Parmi les problm̈es inverses paraboliques considřš figurent le problm̈e classique de retrouver une distribution initiale de la chaleur et la localisation de sources, de chaleur ou de pollution par exemple. Les problm̈es d<U+0019>identification de non linǎritš seront aussi ťudiš. Cet ouvrage s<U+0019>adresse ̉tous ceux qui souhaitent s<U+0019> intřesser ̉l<U+0019>analyse mathm̌atique des problm̈es inverses. This volume is devoted to an introduction of elliptic and parabolic inverse problems. The goal is to present some recent methods for establishing uniqueness and stability results. A number of classical elliptic inverse problems are studied, e.g. the inverse conductivity problem, the detection of corrosion or cracks and inverse spectral problems. Among the parabolic inverse problems, the classic problem of finding an initial distribution of heat and the location of sources is considered. This volume will be of interest to all those who want to learn the mathematical analysis of inverse problems.