{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72530"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72530","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation","abstract":"There are five chapters in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line problem for the Ginzburg-Landau equation are established: (1) local existence-uniqueness; (2) small amplitude solution; (3) criteria for global existence. In Chapter 5, the weak solution to an initial-boundary value problem for the GL equation is obtained via Galerkin's method.","abstract_html":"There are five chapters in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line problem for the Ginzburg-Landau equation are established: (1) local existence-uniqueness; (2) small amplitude solution; (3) criteria for global existence. In Chapter 5, the weak solution to an initial-boundary value problem for the GL equation is obtained via Galerkin's method.","abstract_has_math":false,"creators":["Bu, Qiyue"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Carroll, R."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-17T23:17:43Z","date_published":"2014-12-17T23:17:43Z","updated_at":"2026-07-22T22:26:07Z","subjects":["Applied Mechanics","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9236403"],"render_values":[{"text":"(UMI)AAI9236403","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/72530","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carroll, R."]},{"key":"dc:creator","label":"Author","values":["Bu, Qiyue"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-17T23:17:43Z","10000-01-01","1992"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI9236403","http://hdl.handle.net/2142/72530"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["There are five chapters in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line problem for the Ginzburg-Landau equation are established: (1) local existence-uniqueness; (2) small amplitude solution; (3) criteria for global existence. In Chapter 5, the weak solution to an initial-boundary value problem for the GL equation is obtained via Galerkin's method.","Made available in DSpace on 2014-12-17T23:17:43Z (GMT). No. of bitstreams: 1 9236403.pdf: 2095142 bytes, checksum: d951545107b9dbd217ef54e7dd33522c (MD5) Previous issue date: 1992","Embargo set by: Seth Robbins for item 72698 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","78 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992."]},{"key":"dc:title","label":"Title","values":["On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation"]}]}],"canonical_facts":{"dc:contributor":["Carroll, R."],"dc:creator":["Bu, Qiyue"],"dc:date":["2014-12-17T23:17:43Z","10000-01-01","1992"],"dc:description":["There are five chapters in this thesis. Well-posedness of the forced nonlinear Schrodinger equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line problem for the Ginzburg-Landau equation are established: (1) local existence-uniqueness; (2) small amplitude solution; (3) criteria for global existence. In Chapter 5, the weak solution to an initial-boundary value problem for the GL equation is obtained via Galerkin's method.","Made available in DSpace on 2014-12-17T23:17:43Z (GMT). No. of bitstreams: 1 9236403.pdf: 2095142 bytes, checksum: d951545107b9dbd217ef54e7dd33522c (MD5) Previous issue date: 1992","Embargo set by: Seth Robbins for item 72698 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","78 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992."],"dc:identifier":["(UMI)AAI9236403","http://hdl.handle.net/2142/72530"],"dc:subject":["Applied Mechanics","Mathematics"],"dc:title":["On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:07Z"}