Solution Of Linear Evolution Partial Differential Equations On The Half-Line

Solutions of partial differential equations have presented mathematicians and scientists alike, with unique challenges for centuries. The delicate nature of their solutions require a range of techniques that are highly dependent on initial and boundary conditions. In this thesis, we showcase the shortcomings of using traditional techniques described in literature to solve linear evolution partial differential equations through the heat and wave equations. We investigate how the conditions under which such techniques deteriorate, by attempting to solve the heat equation with nonzero boundary conditions and the Airy equation on the positive real line. Moreover, we observe how such problems give rise to new obstacles in the verification of potential solutions, and highlight the need for the development and implementation of new techniques, such as the Unified Transform method. Lastly, we examine how the Unified Transform method can be invoked to solve initial boundary value problems involving the linear Schrodinger and Airy equations.

Grantor dc:publisher

University of Kansas

Year dc:date.issued

2025

Author dc:creator

• Kyriakidis, Efstratios

Advisor dc:contributor.advisor

• Mantzavinos, Dionyssios

• Mathematics
• Fokas Method
• Partial Differential Equations
• Unified Transform Method

Statement dc:rights

• This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.

Language dc:language.iso

en

Dc Identifier Other

https://www.proquest.com/LegacyDocView/DISSNUM/32042195

OAI identifier oai:identifier

oai:kuscholarworks.ku.edu:1808/38093