Inverse problems are a class of problems in science and engineering where you want to determine phenomena that can only be measured by observing indirect effects.
In theory it is often assumed that infinitely many measurements with infinite precision can be taken. However in practice this is of course not possible.
In this project we will consider a class of inverse boundary value problems where the concrete task is to recover a coefficient in a partial differential equation from knowledge of solutions to the equation at the boundary of the domain. Such problems arise in geophysics and medical imaging.
Of particular interest are problems where only part of the boundary is accessible for measurements. This is a very challenging and ill‐posed problem. Only recently results have started to emerge.
The objective of the project is to develop a mathematical reconstruction algorithm for such inverse boundary value problems with partial data, and then consider the numerical implementation of the algorithm.
Contact person: Kim Knudsen