Generalised and Low-Regularity Solutions of Nonlinear Partial Differential Equations

非线性偏微分方程的广义低正则解

• 批准号: EP/V008889/1
• 负责人: Roger Moser
• 金额: $ 7.05万
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV008889%2F1
• 关键词: Generalised; Low; Regularity; Solutions; Nonlinear

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.

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。对它们的研究已经有数百年了，但仍有许多悬而未决的问题。对于作为本提案主题的方程类型来说尤其如此，即产生广义或低规律性解的非线性方程。 “非线性”意味着各个部分不能简单地相加，而是以更复杂的方式相互作用。术语“广义”和“低规律性解决方案”描述了一种情况，传统的解决方案概念不合适，需要更复杂的概念。英国有几个在该领域拥有强大专业知识的小组，该项目旨在促进新的合作并加强他们之间的现有合作，以及与其他学科的人们建立新的合作。此外，它的目的是为该领域年轻研究人员的培训做出贡献。这将通过组织许多不同形式的研讨会来实现，这些研讨会旨在将这些研究人员聚集在一起。