Nonlinear Evolution Equations

非线性演化方程拟研究摘要gustavo Ponce该项目致力于研究非线性色散方程的各个方面。它将包括几个非线性色散演化方程的薛定谔型的工作。这些出现作为涡丝演化的近似模型，在水波建模中，作为高阶可积系统的例子。研究了非线性色散模型的一些独特的延拓性质。目标是使用这些属性从两个不同时间的解的一些不完全信息中建立关联问题的解的唯一性。所要研究的问题是偏微分方程、经典调和分析和数学物理的交叉。在控制理论的应用中，自然会出现独特的延拓问题。

NONLINEAR EVOLUTION EQUATIONSAbstract of Proposed ResearchGustavo Ponce This project is devoted to research into various aspects of nonlinear dispersive equations. It will include work on several nonlinear dispersive evolution equations of Schroedinger type. These arise as approximate models for the evolution of vortex filaments, in water waves modeling and as examples of higher order integrable systems. Also some unique continuation properties of nonlinear dispersive models will be investigated. The goal is to use these properties to established uniqueness of solutions to an associated problem from some incomplete information of the solutions at two different times.They problems to be investigated are at the intersection of partial differential equations, classical harmonic analysis and mathematical physics. The unique continuation issues arise naturally in control theory applications.