{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86814"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86814","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Interface Dynamics","abstract":"Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.","abstract_html":"Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.","abstract_has_math":false,"creators":["Song, Minsu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Jerrard, Robert L."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:40Z","date_published":"2015-09-28T15:19:40Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3086183"],"render_values":[{"text":"(MiAaPQ)AAI3086183","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86814","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jerrard, Robert L."]},{"key":"dc:creator","label":"Author","values":["Song, Minsu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:40Z","10000-01-01","2003"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86814","(MiAaPQ)AAI3086183"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.","Embargo set by: Seth Robbins for item 88095 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","We present an axiomatic approach to certain geometric evolution problems and associated level set PDEs. We also study threshold dynamics on Rn and cellular automata on certain lattices which satisfy monotonicity, translation invariance and finite propagation speed. We develop the general schemes for the convergence of threshold dynamics and cellular automata to geometric evolutions governed by a velocity function depending on the normal direction alone.","Made available in DSpace on 2015-09-28T15:19:40Z (GMT). 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