Filip Rindler, a Warwick Zeeman Lecturer, has been awarded a 3-year EPSRC Fellowship to investigate Singularities in Nonlinear PDEs which is to start in October 2014 and which includes funding for a related workshop.

This project aims to further the theoretical understanding of singularities, manifested as oscillations and concentrations, in solutions to nonlinear partial differential equations. Since such singularities are not only physically relevant, but also present many technical challenges in the pursuit to prove meaningful assertions about PDEs, this proposal bridges theoretical and applied mathematics. On the applied side, it is related to material microstructure (for example in alloys) and the emergence of complex macroscopic material behaviour from microscopic oscillations. On the theory side, oscillations and concentrations precisely distinguish between weak and strong compactness of sequences in Lebesgue and Sobolev spaces and “quantifying” this difference in a meaningful way is a pivotal goal of this project. Based on recently developed new tools, we aim to improve our understanding of these phenomena and to develop new applications to concrete PDE questions. Collaborations are planned with both applied and theoretical researchers in the field. Furthermore, as part of the grant, a research workshop on the topic will be organised.

EPSRC Grants on the Web site