Nonlinear Evolution Equations

在这个项目中，首席研究员和他的合作者建议开发新的方法和技术，以更好地理解色散模型溶液的定性行为。这些模型描述了相关的物理现象，包括流体力学和波传播中的一些现象。在多学科的方法中，这些创新的方法将改进研究流体动力学中一些突出问题的有效数值工具的设计。此外，他们还将为这些类型的系统的建模和仿真建立新的参数。为了实现上述目标，首席研究员和项目的其他参与者将继续开发主要来自谐波分析的强大分析技术。虽然新方法将集中于具体的非线性问题，但它们的适用性将是广泛的。其他学科的研究人员可能对此感兴趣。首席研究员将通过专业会议和电子出版物的展览尽可能广泛地传播他的研究结果。研究和教育将与促进和扩大代表性不足群体的参与的特别努力、本科生的积极参与、创新的教学倡议和合作方式大力结合起来。

In this project, the principal investigator and his collaborators propose to develop new methods and techniques that will provide a better understanding of the qualitative behavior of solutions of dispersive models. These models describe relevant physical phenomena, including several arising in fluid mechanics and in wave propagation. In a multidisciplinary approach, these innovative methods will improve the design of efficient numerical tools in the study of some outstanding problems in fluids dynamics. Also, they will establish new parameters in the modeling and simulation for these types of systems.To achieve the aforementioned goals, the principal investigator and the project's other participants will continue the development of powerful analytic techniques mainly coming from harmonic analysis. While the new approaches will be focused in concrete nonlinear problems, their applicability will be broad. This is of potential interest to researchers in other disciplines. The principal investigator will disseminate his results as widely as possible through expositions at professional meetings and electronic publications. Research and education will be vigorously integrated with special efforts to promote and broaden the participation of underrepresented groups, with the active participation of undergraduates, with innovative pedagogical initiatives and modes of collaboration.