Sloshing of shallow water on a bounded domain

本课题是对线性和非线性双曲型偏微分方程集理论和应用于一体的研究。在研究了项目第一部分的浅水晃动后，我们现在考虑更一般的双曲型系统。我们的目标是使用几何光学展开方法来分析这类系统的稳定性。这将从观察对称双曲型系统开始，目标是将那里学到的东西应用到具有不同性质的方程中。这将与以前对浅水晃动的研究相一致，因为这是该方法可以应用于的系统类型的一个例子。主要目的是发展关于双曲型方程的严格理论。这项研究的应用包括描述流体流动的基本方程是双曲型的任何物理问题，例如容器中水或气体的晃动。

This project is a study of linear and nonlinear hyperbolic partial differential equations, combining both theory and applications. After looking at sloshing of shallow water in a vessel for the first part of the project we now consider more general hyperbolic systems. We aim to analyse the stability of such systems using a geometric optics expansion method. This will begin with looking at symmetric hyperbolic systems with the goal of applying what is learned there to equations with different properties. This will tie in with the previous research on the shallow water sloshing as that is an example of the type of system that this method can be applied to. The main aim being to develop rigorous theory regarding equations of hyperbolic type. Applications of the research include any physical problem where the underlying equations that describe the fluid flow are of hyperbolic type, e.g. sloshing of water or gas in a container.