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Publication status	Unpublished - 2002

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This thesis has been made available in the UWA Profiles and Research Repository as part of a UWA Library project to digitise and make available theses completed before 2003. If you are the author of this thesis and would like it removed from the UWA Profiles and Research Repository, please contact digitaltheses-lib@uwa.edu.au

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10.26182/5d4788bbf2416

Anderson_M_L_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.",

author = "Anderson, {Michael Lindsay}",

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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.

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