Ill posed inverse problems

For a long time mathematicians felt that ill-posed problems cannot describe real phenomena and objects. However [...] the class of ill-posed problems includes many classical mathematical problems and, most significantly, that such problems have important applications. Tikhonov

Inverse problems are concerned with determining causes for a desired or an observed effect or calibrating the parameters of a mathematical model to reproduce observations. Inverse problems most often do not fulfill Hadamard's postulates of well-posedness: they might not have a solution in the strict sense, solutions might not be unique and/or might not depend continuously on the data. Hence their mathematical analysis is subtle. However they have many applications in engineering, physics and other fields. Here are some web ressources on Ill posed inverse problems.

Course page on: Inverse Problem in Financial Modeling.

Conference on Ill posed Inverse problems, (August 5-9 2002) Sobolev Institute of Mathematics, Novosibirsk, Russia.

Journals and Book Series:

Inverse Problems.
Journal of Inverse and Ill posed problems
Inverse Problems in Engineering.
The Inverse and Ill posed Problems book series

Web sites dedicated to ill posed inverse problems:

University of Linz (Austria) Inverse Problems Homepage
University of Alabama Inverse Problem Homepage
American Group for Inverse Problems in Engineering
Inverse Problem Network : a network for researchers working the area of
Inverse and/or Ill-Posed Problems.
Finnish Inverse Problem Society.

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