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，特别是来自科学界代表性不足群体的研究生、初级研究人员、女性和数学家提供支持，以参加将在堪萨斯大学举行的第四届 KUMUNU 偏微分方程、动力系统和应用年度会议2018年4月21-22日。​本次会议由堪萨斯大学（KU）、密苏里大学（MU）和内布拉斯加大学（NU）的教师共同主办。几乎所有物理现象都受基本定律和设计原理的约束，这些定律和设计原理将一个量的变化率与其他量的变化率直接联系起来​​这一强大的想法自然而然地产生了微分方程，微分方程被广泛用作数学物理中的模型，并且具有潜力。该会议将汇集来自堪萨斯州、密苏里州和内布拉斯加州附近地理区域的研究人员，交流想法并报告新成果。微分方程和基于该系列会议之前三场会议的成功，该会议将为地区初级和高级研究人员以及研究生提供一个讨论各自领域的最新进展和挑战的场所。将有机会展示他们的工作并通过与该领域的资深专家互动来深入了解这一重要主题。参见 http://dept.ku.edu/~math/conferences/2018/KUMUNUPDE/ 复杂的非线性系统在科学和工程中比比皆是，它们的行为通常由非线性偏微分方程 (PDE) 系统建模。了解其解决方案的行为对于各种实际应用（包括流体流动、火焰前沿传播和光纤通信）至关重要。许多偏微分方程可以方便地描述为无限维动力系统，从而允许使用动力系统理论中的工具和方法对这些系统的解（如不变流形）进行定性和定量预测对于理解有限维动力系统的行为有很大帮助，但非线性偏微分方程和动力学之间的联系。系统仍然是当前活跃的研究领域，在过去的几十年中，这些领域的研究人员及其应用领域的研究人员之间的合作在我们对动态行为、稳定性和鲁棒性的理解方面取得了巨大进展。连贯的本次会议的主题包括（i）流体动力学、水波和色散偏微分方程，（ii）耗散系统中非线性波的存在、动力学和稳定性，以及（iii）动力系统、不变流形和吸引子。​这些主题在区域专家以及受邀全体会议演讲者中得到了很好的体现。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准。