The main topic in the basic research of the Chair for Industrial Mathematics is the treatment of inverse and ill-posed problems. Inverse problems are concerned with determining causes for a desired or an observed effect. Inverse problems most often do not fulfill Hadamard's postulates of well-posedness . Mathematically, this leads to the problem of inverting the Radon transform .
Similar problems appear in non-destructive testing.
This has important industrial applications e.g. in continuous casting of steel . From measurements of waves scattered by an obstacle, one wants to determine e.g. the shape or the location of this obstacle. Problems of this type appear also in the exploration of minerals or oil. This is of great interest in medical and pharmaceutical research for analysing the structure of and the interaction between proteins. All these problems are ill-posed .