{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/38093"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/38093","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"Solution Of Linear Evolution Partial Differential Equations On The Half-Line","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Kyriakidis, Efstratios"],"institution":"University of Kansas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Mantzavinos, Dionyssios"],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05-31","date_published":"2025-05-31","updated_at":"2026-07-24T02:45:19Z","subjects":["Mathematics","Fokas Method","Partial Differential Equations","Unified Transform Method"],"languages":["en"],"rights":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32042195"],"render_values":[{"text":"https://www.proquest.com/LegacyDocView/DISSNUM/32042195","href":"https://www.proquest.com/LegacyDocView/DISSNUM/32042195","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1808/38093","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Mantzavinos, Dionyssios"]},{"key":"dc:creator","label":"Author","values":["Kyriakidis, Efstratios"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-22T20:39:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-22T20:39:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-05-31"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Fokas Method","Partial Differential Equations","Unified Transform Method"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32042195"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1808/38093"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Solution Of Linear Evolution Partial Differential Equations On The Half-Line"]}]}],"canonical_facts":{"dc:contributor.advisor":["Mantzavinos, Dionyssios"],"dc:creator":["Kyriakidis, Efstratios"],"dc:date.accessioned":["2026-04-22T20:39:30Z"],"dc:date.available":["2026-04-22T20:39:30Z"],"dc:date.issued":["2025-05-31"],"dc:description.abstract":["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."],"dc:identifier.other":["https://www.proquest.com/LegacyDocView/DISSNUM/32042195"],"dc:identifier.uri":["https://hdl.handle.net/1808/38093"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:rights":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."],"dc:subject":["Mathematics","Fokas Method","Partial Differential Equations","Unified Transform Method"],"dc:title":["Solution Of Linear Evolution Partial Differential Equations On The Half-Line"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T02:45:19Z"}