Boundary tracing is a technique that has been used in an ad hoc manner by several authors in their investigations of PDE behaviour [1, 20, 22]. In this thesis a general framework for the technique is developed for two dimensional second order PDEs. Interesting aspects are illustrated through an extensive collection of simple examples. Boundary tracing is then used to derive new results for a variety of PDEs, including the derivation of new domains admitting exact solutions for the non-linear Laplace-Young equation. These new domains are the only known examples with corners. As such they provide new and verify known results regarding corner behaviour. New results regarding rough surfaces and smooth corners are developed. Extensions of boundary tracing to higher dimensions and higher order equations are also discussed.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2002|