{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71222"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71222","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips","abstract":"We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.","abstract_html":"We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.","abstract_has_math":false,"creators":["Challener, David Carroll"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:10Z","date_published":"2014-12-16T06:18:10Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8502093"],"render_values":[{"text":"(UMI)AAI8502093","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71222","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Challener, David Carroll"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:10Z","10000-01-01","1984"]},{"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":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71222","(UMI)AAI8502093"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.","We obtain results on convergence of the eigenfunction expansion resulting from separation of variables. Results are shown when the summability method of Riesz Typical Means is applied to the resulting series and L('p) norm convergence results are given. St. Venant's principle is exhibited along with semi-group properties of solutions and then all results are applied to rectangular regions.","Made available in DSpace on 2014-12-16T06:18:10Z (GMT). No. of bitstreams: 1 8502093.pdf: 2668882 bytes, checksum: 60c7e12ac09bb300d8f2ecdfd4151442 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71388 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","151 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."]},{"key":"dc:title","label":"Title","values":["Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips"]}]}],"canonical_facts":{"dc:creator":["Challener, David Carroll"],"dc:date":["2014-12-16T06:18:10Z","10000-01-01","1984"],"dc:description":["We consider the problem (DELTA)('2)(w(x,y)) = 0, w((+OR-)1,y) = w(,x)((+OR-)1,y) = 0 with boundary conditions w(,xx)(x,0) = f(x) w(,yy)(x,0) = g(x) on the semi-infinite strip -1 (LESSTHEQ) x (LESSTHEQ) 1, 0 < y.","We obtain results on convergence of the eigenfunction expansion resulting from separation of variables. Results are shown when the summability method of Riesz Typical Means is applied to the resulting series and L('p) norm convergence results are given. St. Venant's principle is exhibited along with semi-group properties of solutions and then all results are applied to rectangular regions.","Made available in DSpace on 2014-12-16T06:18:10Z (GMT). No. of bitstreams: 1 8502093.pdf: 2668882 bytes, checksum: 60c7e12ac09bb300d8f2ecdfd4151442 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71388 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","151 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."],"dc:identifier":["http://hdl.handle.net/2142/71222","(UMI)AAI8502093"],"dc:subject":["Mathematics"],"dc:title":["Convergence Properties of the Eigenfunction Expansion of the Biharmonic Equation on Rectangular and Semi-Infinite Strips"],"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":"2026-07-22T22:26:04Z"}