It is a common practice to reconstruct events from the past on the basis of a number of facts in
the present, for example, to determine the cause of a disease based on the results of a medical
examination. In science, such a problem is referred to as an inverse problem.
It is easy to make a mistake when solving inverse problems. For example, symptoms that are
associated with an HIV infection look like symptoms of other illnesses. It is thus impossible to tell,
exclusively on the basis of symptoms, whether the problem is related to HIV or another medical
condition. Therefore, the problem of determining the cause of a disease is called ill-posed, i.e.
there is no unique cause (or solution). Additional medical investigations (measurements) are
required to determine the correct cause.
Similar issues are encountered in the inverse problems considered in this project. First, several
inverse problems with applications in mechanics are studied. Secondly, as far as we know for the
very first time, inverse problems in time-varying domains will be tackled.
For each problem under consideration, the most important questions are:
(1) Which additional measurement is required for the unique reconstruction of the solution?
(2) How can the solution be reconstructed?
In this project, these questions will be investigated by using advanced mathematical techniques
and by developing numerical methods to calculate the required information.