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。它们已被研究了数百年，但仍有许多悬而未决的问题。这对于作为本提案主题的方程类型尤其如此，即产生广义或低正则解的非线性方程。“非线性”意味着各个部分不能简单地相加，而是以一种更复杂的方式相互作用。术语“一般化”和“低正则性解”描述了一种情况，即解决方案的传统概念不合适，需要更复杂的概念。英国有几个在这一领域拥有强大专业知识的小组，该项目旨在促进新的合作，加强他们之间的现有合作，以及与其他学科的人建立新的合作。此外，它旨在促进该领域年轻研究人员的培训。这将通过组织一些旨在将这些研究人员聚集在一起的各种形式的讲习班来实现。

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.