Boundary tracing methods of partial differential equations

Michael Lindsay Anderson

doi:10.26182/5d4788bbf2416

Boundary tracing methods of partial differential equations

Michael Lindsay Anderson

Research output: Thesis › Doctoral Thesis

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Abstract

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.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	The University of Western Australia
DOIs	https://doi.org/10.26182/5d4788bbf2416
Publication status	Unpublished - 2002

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Cite this

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title = "Boundary tracing methods of partial differential equations",

abstract = "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.",

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AB - 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.

U2 - 10.26182/5d4788bbf2416

DO - 10.26182/5d4788bbf2416

M3 - Doctoral Thesis

ER -

Boundary tracing methods of partial differential equations

Abstract

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