Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations

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Partial differential equations underpin many problems in all sciences as well as economics, social sciences, and other disciplines. They have been studied for hundreds of years, but there are still many open questions. This is particularly the case for the type of equations that are the subject of this proposal, namely nonlinear equations giving rise to generalised or low-regularity solutions. "Nonlinear" means that the the individual parts cannot simply be added up, but interact with each other in a more complex way. The terms "generalised" and "low-regularity solutions" describe a situation where conventional notions of a solution are inappropriate and more sophisticated concepts are required.The UK has several groups with strong expertise in this area, and this project aims to facilitate new collaborations and strengthen existing collaborations between them, as well as establish new collaborations with people from other disciplines. Furthermore, it aims to contribute to the training of young researchers in the area. This will be achieved by organising a number of workshops of various formats designed to bring these researchers together.