Nonlinear partial differential equations and propagation phenomena

非线性偏微分方程和传播现象

• 批准号: DP220101820
• 负责人: Prof Yihong Du
• 金额: $ 29.06万
• 依托单位: The University of New England
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220101820
• 关键词: Nonlinear; partial; differential; equations; propagation

This project of strategic basic research aims to develop new mathematics in nonlinear partial differential equations to better understand the propagation phenomena arising in a variety of applications, such as the spreading of infectious diseases or cancerous cells, or the invasion of alien species. New models of partial differential equations over spatial regions with moving boundaries will be introduced and systematically studied to provide deep understanding of the mechanisms of important new phenomena in propagation, including accelerated spreading and the onset of such spreading. The mathematical questions are concerned with the long-time dynamics of equations with free boundary, and the asymptotic profiles of their solutions.

这一战略性基础研究项目旨在发展非线性偏微分方程的新数学，以更好地理解在各种应用中出现的传播现象，如传染病或癌细胞的传播，或外来物种的入侵。文中将介绍和系统地研究具有移动边界的空间区域上的偏微分方程的新模型，以深入理解传播中重要的新现象的机制，包括加速传播和这种传播的开始。这些数学问题涉及具有自由边界的方程的长时间动力学及其解的渐近轮廓。