KUMU PDE Conference Proposal

KUMU PDE 会议提案

• 批准号: 1500607
• 负责人: Milena Stanislavova
• 金额: $ 1.55万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-04-01 至 2016-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500607&HistoricalAwards=false
• 关键词: KUMU; PDE; Conference; Proposal

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 regional conference "KUMU Conference in PDE, Dynamical Systems and Applications" to be held at the University of Kansas from April 18-19, 2015, co-organized by faculty from the University of Kansas (KU) and the University of Missouri (MU). Nearly all important physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of some quantity to that of some other quantity. Indeed, given the initial conditions and the physical laws of motion one seeks to predict the future and reconstruct the past. This important observation naturally leads to the idea of a differential equation, thus providing the key to understanding many real-world problems. Differential equations 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 for modeling signals in optical communication networks. This conference will facilitate greater interaction between researchers in differential equations and its related fields from the area close to Kansas and Missouri. Planned as the first of a series of annual meetings, the conference will provide a venue for regional junior and established researchers, as well as graduate students to discuss the recent advances and challenges in their respective fields. In addition, young researchers will be given the opportunity to present their own work and to gain insights into this important subject through interactions with senior experts in the field. The conference website: https://www.math.ku.edu/conferences/2015/KUMUPDE/index.htmlComplex 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's and dynamical systems is still an area 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 main themes of this conference include (i) fluid dynamics, water waves and dispersive PDE's, (ii) existence, dynamics, and stability of nonlinear waves in dissipative systems, and (iii) dynamical systems and 2d-Navier Stokes equations.The techniques used to solve many challenging problems in these broad areas often combine ideas and methodologies from dynamical systems and partial differential equations together with probability theory, spectral and functional analysis, Evans functions, and geometric singular perturbation theory, to name a few.

该奖项将为参与者，特别是研究生，初级研究人员，妇女和数学家的科学群体，以参加“ PDE的KUMU会议，动态系统和应用”的区域会议，将于2015年4月18日至19日在堪萨斯大学举行，从2015年4月18日至19日，由Kansas和Kansas（Kansas of Kansas）（MISSU）（MISSU）（MISSU）（MISSU）（KU）（MISSU）（MISSU）（MISSU）（MISSU）（MISSU）（MISSU）（ku）（ku）（ku）（ku）（ku）（ku）（ku）（ku）。 几乎所有重要的物理现象都受基本定律和设计原则的管辖，这些定律和设计原则将某些数量的变化率与其他数量的变化率直接相关。 确实，鉴于最初的条件和运动定律，人们试图预测未来并重建过去。 这种重要的观察自然会导致差分方程的概念，从而为理解许多现实世界问题提供了关键。 微分方程在数学物理学中被广泛用作模型，并在包括Bose-Einstein冷凝物，流体动力学，模式形成，气体动力学以及在光学通信网络中建模信号在内的许多领域具有潜在的应用。这次会议将促进从堪萨斯州和密苏里州附近的微分方程中的研究人员之间的更大互动及其相关领域。该会议计划作为一系列年度会议中的第一次，将为区域初级和成熟的研究人员以及研究生提供一个地点，以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通过与该领域的高级专家进行互动来展示自己的作品并深入了解这一重要主题。会议网站：https：//www.math.ku.edu/conferences/2015/kumupde/index.htmlcomplex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）的系统建模。 对于了解各种实际应用，包括流体流，火焰前端传播和光纤通信，对理解解决方案行为的任何进展至关重要。 许多PDE可以方便地描述为无限尺寸动态系统，从而允许使用动态系统理论中的工具和方法来对这些系统的解决方案做出定性和定量预测。 诸如不变歧管之类的对象非常有助于理解有限维动力学系统的行为，但是非线性PDE和动力学系统之间的连接仍然是一个积极的当前研究。 在过去的几十年中，这些领域的研究人员以及在其应用中工作的研究人员之间的合作在我们对这种非线性PDE中相干结构的动态行为，稳定性和鲁棒性方面为我们提供了巨大的进步。 这次会议的主要主题包括（i）流体动态，水波和散热性PDE，（ii）非线性波在耗散系统中的存在，动态和稳定性，以及（iii）动力学系统和2D-Navier Stokes方程。用于在这些广泛的概念和方法中融合了许多挑战性问题的技术，并分别构成了这些概率和方法，并将各种概念的范围融合在一起，并分别融合了动态学的范围，并分别构成了界面的范围，并分别构成了分析性的范围，并分别融合了概念的范围和分析性。分析，Evans功能和几何奇异扰动理论仅举几例。