Partial differential equations form the foundation of our modern scientific understanding of the world.
The laws of nature are written in the language of differential equations and a rigorous mathematical
understanding of this kind of equations is instrumental for progress in science as a whole. Partial
differential equations describe a wide variety of phenomena and can therefore not be solved in a naive
sense of the word. Consequently, the mathematical analysis is not concerned with finding solutions but
rather with the development of a general theory that yields conditions under which solutions exist at all
and they are unique. Already for many basic equations the traditional pen-and-paper approach of
mathematics is not powerful enough to make progress. Thus, the goal of the research project is develop
novel computer-assisted techniques to augment the traditional approach. This is supposed to break new
ground and make it possible to approach problems that are completely inaccessible to traditional pen-
and-paper mathematics so far.