4th Annual KUMUNU Conference in Partial Differential Equations, Dynamical Systems and Applications

第四届偏微分方程、动力系统和应用 KUMUNU 年度会议

• 批准号: 1753332
• 负责人: Mathew Johnson
• 金额: $ 1.77万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-03-01 至 2019-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1753332&HistoricalAwards=false
• 关键词: 4th; Annual; KUMUNU; Conference; Partial

This award will provide support for participants, especially graduate students, junior researchers, women and mathematicians from under-represented groups in the sciences, to attend the 4th Annual KUMUNU Conference on PDE, Dynamical Systems, and Applications to be held at the University of Kansas on April 21-22, 2018.  This conference is co-organized by faculty from the University of Kansas (KU), the University of Missouri (MU), and the University of Nebraska (NU).  Nearly all physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of one quantity to that of some other quantity.  This powerful idea leads naturally to differential equations, which are widely used as models in mathematical physics and have potential applications to many fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics, and fiber optical communication.  This conference will bring together researchers from the geographic area close to Kansas, Missouri and Nebraska to exchange ideas and report new results in differential equations and applications.  Building on the success of the three prior conferences in this conference series, the conference will provide a venue for regional junior and senior researchers, as well as graduate students, to discuss recent advances and challenges in their respective fields.  Additionally, young researchers will be given the opportunity to present their work and to gain insight into this important subject through interactions with senior experts in the field.  The conference website can be found at http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/Complex nonlinear systems abound in science and engineering, and their behavior is often modeled by systems of nonlinear partial differential equations (PDE). Any progress towards understanding the behavior of their solutions is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communication. Many PDE can be conveniently described as infinite dimensional dynamical systems, allowing for the use of tools and methodologies from dynamical systems theory to make qualitative and quantitative predictions about the solutions of these systems. Objects like invariant manifolds have been a great aid in understanding the behavior of finite-dimensional dynamical systems, but the connections between nonlinear PDE and dynamical systems is still an area of active current research. In the last few decades, collaborations between researchers in these fields, as well as with those working in their applications, have provided tremendous progress in our understanding of the dynamical behavior, stability and robustness of coherent structures in such nonlinear PDE.  The themes of this conference include (i) fluid dynamics, water waves and dispersive PDE, (ii) existence, dynamics and stability of nonlinear waves in dissipative systems, and (iii) dynamical systems, invariant manifolds and attractors.  These themes are well represented by the regional experts as well as the invited plenary speakers.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项将为参与者提供支持，特别是研究生，初级研究人员，妇女和数学家从科学代表性不足的群体，参加第四届年度KUMUNU会议PDE，动力系统和应用将于2018年4月21日至22日在堪萨斯大学举行。 本次会议由堪萨斯大学（KU）、密苏里州大学（MU）和内布拉斯加大学（NU）的教师共同组织。 几乎所有的物理现象都受到基本定律和设计原则的支配，这些基本定律和设计原则将一个量的变化率与另一个量的变化率直接联系起来。 这个强大的想法自然导致微分方程，它被广泛用作数学物理中的模型，并在许多领域有潜在的应用，包括玻色-爱因斯坦凝聚，流体动力学，图案形成，气体动力学和光纤通信。 本次会议将汇集来自地理区域接近堪萨斯，密苏里州和内布拉斯加州的研究人员交流思想，并报告微分方程和应用的新成果。 在此系列会议之前三次会议成功的基础上，会议将为区域初级和高级研究人员以及研究生提供一个场所，讨论各自领域的最新进展和挑战。 此外，年轻的研究人员将有机会介绍他们的工作，并通过与该领域的高级专家互动来深入了解这一重要课题。 会议网站可以在http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/Complex上找到，非线性系统在科学和工程中大量存在，它们的行为通常由非线性偏微分方程（PDE）系统建模。对理解其解决方案的行为的任何进展对于各种实际应用都至关重要，包括流体流动，火焰前锋传播和光纤通信。许多偏微分方程可以方便地描述为无限维动力系统，允许使用动力系统理论的工具和方法来对这些系统的解进行定性和定量预测。像不变流形这样的对象在理解有限维动力系统的行为方面有很大的帮助，但是非线性PDE和动力系统之间的联系仍然是当前研究的一个活跃领域。在过去的几十年里，这些领域的研究人员之间的合作，以及与那些在他们的应用工作，提供了巨大的进步，在我们的理解的动力学行为，稳定性和鲁棒性的相干结构在这样的非线性偏微分方程。 本次会议的主题包括（i）流体动力学，水波和色散PDE，（ii）耗散系统中非线性波的存在性，动力学和稳定性，以及（iii）动力系统，不变流形和吸引子。 该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。