{"id":{"repo_id":"cornell","oai_identifier":"oai:ecommons.cornell.edu:1813/10739"},"canonical_url":"https://search.dev.ndltd.org/etd/cornell/oai:ecommons.cornell.edu:1813/10739","repository":{"repo_id":"cornell","name":"Cornell University","base_url":"https://ecommons.cornell.edu/server/oai/request"},"display":{"title":"Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation","abstract":"This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being finite. A novel asymptotic-numeric matching scheme is used to uncover delicate bifurcation behavior in the equilibria. The exact nature of this bifurcation behavior leads to a demonstration that the equilibria are degenerate critical points in the sense of Morse. Finally, the space of heteroclinic orbits is shown to have a cell complex structure, which is finite dimensional when the number of equilibria is finite.","abstract_html":"This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being finite. A novel asymptotic-numeric matching scheme is used to uncover delicate bifurcation behavior in the equilibria. The exact nature of this bifurcation behavior leads to a demonstration that the equilibria are degenerate critical points in the sense of Morse. Finally, the space of heteroclinic orbits is shown to have a cell complex structure, which is finite dimensional when the number of equilibria is finite.","abstract_has_math":false,"creators":["Robinson, Michael"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-04-25T17:51:51Z","date_published":"2008-04-25T17:51:51Z","updated_at":"2026-07-24T01:48:56Z","subjects":["Floer homology","semilinear parabolic equation","blow-up behavior","IMEX method","asymptotic series"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/1813/10739","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Robinson, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2008-04-25T17:51:51Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-04-25T06:11:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2008-04-25T17:51:51Z"]},{"key":"dc:type","label":"Dc Type","values":["dissertation or thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Floer homology","semilinear parabolic equation","blow-up behavior","IMEX method","asymptotic series"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1813/10739"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being finite. A novel asymptotic-numeric matching scheme is used to uncover delicate bifurcation behavior in the equilibria. The exact nature of this bifurcation behavior leads to a demonstration that the equilibria are degenerate critical points in the sense of Morse. Finally, the space of heteroclinic orbits is shown to have a cell complex structure, which is finite dimensional when the number of equilibria is finite."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation"]}]}],"canonical_facts":{"dc:creator":["Robinson, Michael"],"dc:date.accessioned":["2008-04-25T17:51:51Z"],"dc:date.available":["2013-04-25T06:11:45Z"],"dc:date.issued":["2008-04-25T17:51:51Z"],"dc:description.abstract":["This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being finite. A novel asymptotic-numeric matching scheme is used to uncover delicate bifurcation behavior in the equilibria. The exact nature of this bifurcation behavior leads to a demonstration that the equilibria are degenerate critical points in the sense of Morse. Finally, the space of heteroclinic orbits is shown to have a cell complex structure, which is finite dimensional when the number of equilibria is finite."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://hdl.handle.net/1813/10739"],"dc:language.iso":["en_US"],"dc:subject":["Floer homology","semilinear parabolic equation","blow-up behavior","IMEX method","asymptotic series"],"dc:title":["Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation"],"dc:type":["dissertation or thesis"]},"updated_at":"2026-07-24T01:48:56Z"}