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.

部分微分方程是所有科学以及经济学，社会科学和其他学科的许多问题的基础。他们已经研究了数百年，但仍然有许多开放问题。对于该提案的主题，即非线性方程的主题的方程类型尤其如此，从而产生了广义或低规范的解决方案。 “非线性”是指单个部分不能简单地添加，而是以更复杂的方式相互交互。术语“广义”和“低规范性解决方案”描述了一种情况，即解决方案的传统概念是不适当的，并且需要更复杂的概念。英国在该领域中拥有多个具有强大专业知识的群体，该项目旨在促进新的合作并加强他们之间的现有合作，并与其他人民建立新的合作。此外，它旨在为该地区的年轻研究人员培训。这将通过组织许多旨在将这些研究人员聚集在一起的各种格式的研讨会来实现。