Sloshing of shallow water on a bounded domain

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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.