Mathematical Sciences: Some Nonlinear Problems In Differential and Integral Equations

在这个项目中，主要研究人员将分析 非线性微分积分四题 方程 第一个问题是一个积分微分方程 它描述了一个楔子进入一个水池。 的 第二个问题涉及使用同伦方法来研究 积分方程行波解的存在性， 微分方程的应用。 第三 问题涉及使用射击方法来研究 混沌轨道的行为 最后是第四个问题 关于寻找一些二维问题的相似解， Navier-Stokes方程。 许多描述这种行为的数学模型 日常现象涉及积分方程或微分方程 方程或这两种类型的方程的组合。 非常 研究这类方程的解往往是最容易的 定性地，也就是说，而不是寻找精确的分析， 或者数值解，可能会非常复杂， 对于包含的解的近似表示， 或多或少，精确解的本质。 在这个项目中 主要研究者将采用定性方法进行研究， 积分和微分方程的解 流体动力学，生物学和力学

In this project the principal investigators will analyze four problems involving nonlinear differential and integral equations. The first problem is an integro-differential equation that describes the entry of a wedge into a bath of water. The second problem involves the use of homotopy methods to study the existence of travelling wave solutions of integral and differential equations that arise in applications. The third problem involves the use of shooting methods to study the behavior of chaotic orbits. And finally the fourth problem concerns finding similarity solutions of some two-dimensional versions of the Navier-Stokes equations. Many of the mathematical models that describe the behavior of everyday phenomena involve integral equations or differential equations or combinations of these two types of equations. Very often it is easiest to study the solutions of such equations qualitatively, that is, instead of looking for exact analytical or numerical solutions that can be quite complicated, one looks for approximate representations of the solutions that contain, more or less, the essence of the exact solution. In this project the principal investigators will use qualitative methods to study the solutions of integral and differential equations that arise in fluid dynamics, biology and mechanics.