Philipp di Dio

In this project I want to investigate time-dependent moments of distributions (functions) from partial differential equations. Recently moment problem implementations showed the usefulness to find solutions of partial differential equations. I extended the moment problem in a systematic and general way to derivatives of moments and proved the existence of solutions of a PDE. Both methods (the moment theoretic and the PDE methods) shall be combined in this project to improve the theoretical foundation of moment problem implementations for PDEs. Hence, the field of the moment problem and the field of partial differential equations will benefit from the results of this project. The University of Konstanz provides the perfect research environment for this project since it has with Prof. S. Kuhlmann and Prof. M. Schweighofer strong active researchers in the field of the moment problem and students are provided with a lecture about the moment problem. As an additional very active researcher in the field of the moment problem the applicant will cooperate with Prof. R. Curto from the University of Iowa, USA, on this project.