Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations

偏微分方程是所有科学以及经济学、社会科学和其他学科中许多问题的基础。他们已经研究了几百年，但仍然有许多悬而未决的问题。这是特别是这种情况下的类型的方程，这是本建议的主题，即非线性方程产生广义或低正则性的解决方案。“非线性”意味着各个部分不能简单地相加，而是以更复杂的方式相互作用。术语“广义”和“低正则性解”描述了一种情况，即传统的解的概念是不合适的，需要更复杂的概念。英国有几个在这一领域具有很强专业知识的小组，本项目旨在促进新的合作，加强他们之间的现有合作，并与其他学科的人建立新的合作。此外，它还致力于培训该领域的年轻研究人员。这将通过组织旨在将这些研究人员聚集在一起的各种形式的研讨会来实现。

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.