{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71230"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71230","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Exponential Decay for the Saint-Venant Principle","abstract":"We consider a semi-infinite beam B = {(z,t)(VBAR)z(ELEM)(OMEGA), t (GREATERTHEQ) 0} where (OMEGA) is a bounded domain in (//R)('2) with the cone property and a C('3)-smooth boundary. By applying semigroup theory and spectral theory, we show that in our formulation Saint-Venant's principle is true for a class of stored energy functions of the type W = 1/2u('2) + Q(u(,,1),u(,,2)), where u is the displacement along the t-axis. By using the theory of stable manifolds, we also prove the existence of a mild solution for the associated traction boundary value problem in elastostatics.","abstract_html":"We consider a semi-infinite beam B = {(z,t)(VBAR)z(ELEM)(OMEGA), t (GREATERTHEQ) 0} where (OMEGA) is a bounded domain in (//R)('2) with the cone property and a C('3)-smooth boundary. By applying semigroup theory and spectral theory, we show that in our formulation Saint-Venant's principle is true for a class of stored energy functions of the type W = 1/2u('2) + Q(u(,,1),u(,,2)), where u is the displacement along the t-axis. By using the theory of stable manifolds, we also prove the existence of a mild solution for the associated traction boundary value problem in elastostatics.","abstract_has_math":false,"creators":["Wu, Jinn Wen"],"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":"2014-12-16T06:18:12Z","date_published":"2014-12-16T06:18:12Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8502348"],"render_values":[{"text":"(UMI)AAI8502348","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71230","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wu, Jinn Wen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:12Z","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/2142/71230","(UMI)AAI8502348"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We consider a semi-infinite beam B = {(z,t)(VBAR)z(ELEM)(OMEGA), t (GREATERTHEQ) 0} where (OMEGA) is a bounded domain in (//R)('2) with the cone property and a C('3)-smooth boundary. By applying semigroup theory and spectral theory, we show that in our formulation Saint-Venant's principle is true for a class of stored energy functions of the type W = 1/2u('2) + Q(u(,,1),u(,,2)), where u is the displacement along the t-axis. By using the theory of stable manifolds, we also prove the existence of a mild solution for the associated traction boundary value problem in elastostatics.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). 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By applying semigroup theory and spectral theory, we show that in our formulation Saint-Venant's principle is true for a class of stored energy functions of the type W = 1/2u('2) + Q(u(,,1),u(,,2)), where u is the displacement along the t-axis. By using the theory of stable manifolds, we also prove the existence of a mild solution for the associated traction boundary value problem in elastostatics.","Made available in DSpace on 2014-12-16T06:18:12Z (GMT). No. of bitstreams: 1 8502348.pdf: 2309266 bytes, checksum: 7ff5a5ff50260f14a844971444938699 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 71396 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","142 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."],"dc:identifier":["http://hdl.handle.net/2142/71230","(UMI)AAI8502348"],"dc:subject":["Mathematics"],"dc:title":["Exponential Decay for the Saint-Venant Principle"],"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"}