{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/39323"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/39323","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"On the Stability of Solutions to a Phase Transition Model","abstract":"We will discuss the stability of certain solutions to a phase transition model. This model is typically expressed as a partial differential equation: <italic> u<sub>t</sub> = &epsilon;<super>2</super>u<sub>xx</sub>-F'(u), u<sub>x</sub>(0) = u<sub>x</sub>(1) = 0, </italic> where <italic> F(u) </italic> is a so-called \"double-well'' potential. We consider both classical and nonclassical examples for F. Furthermore, the main method we use in this discussion of stability is that of upper and lower solutions.","abstract_html":"We will discuss the stability of certain solutions to a phase transition model. This model is typically expressed as a partial differential equation: &lt;italic&gt; u&lt;sub&gt;t&lt;/sub&gt; = &amp;epsilon;&lt;super&gt;2&lt;/super&gt;u&lt;sub&gt;xx&lt;/sub&gt;-F&#x27;(u), u&lt;sub&gt;x&lt;/sub&gt;(0) = u&lt;sub&gt;x&lt;/sub&gt;(1) = 0, &lt;/italic&gt; where &lt;italic&gt; F(u) &lt;/italic&gt; is a so-called &quot;double-well&#x27;&#x27; potential. We consider both classical and nonclassical examples for F. Furthermore, the main method we use in this discussion of stability is that of upper and lower solutions.","abstract_has_math":false,"creators":["Hardeman, Heather Katelyn"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-27T22:01:46Z","subjects":["analysis"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/39323","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hardeman, Heather Katelyn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-07-10T08:35:41Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-10T08:35:41Z"]},{"key":"dc:date.issued","label":"Date","values":["2014"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/39323"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We will discuss the stability of certain solutions to a phase transition model. This model is typically expressed as a partial differential equation: <italic> u<sub>t</sub> = &epsilon;<super>2</super>u<sub>xx</sub>-F'(u), u<sub>x</sub>(0) = u<sub>x</sub>(1) = 0, </italic> where <italic> F(u) </italic> is a so-called \"double-well'' potential. We consider both classical and nonclassical examples for F. Furthermore, the main method we use in this discussion of stability is that of upper and lower solutions."]},{"key":"dc:title","label":"Title","values":["On the Stability of Solutions to a Phase Transition Model"]}]}],"canonical_facts":{"dc:creator":["Hardeman, Heather Katelyn"],"dc:date.accessioned":["2014-07-10T08:35:41Z"],"dc:date.available":["2014-07-10T08:35:41Z"],"dc:date.issued":["2014"],"dc:description.abstract":["We will discuss the stability of certain solutions to a phase transition model. This model is typically expressed as a partial differential equation: <italic> u<sub>t</sub> = &epsilon;<super>2</super>u<sub>xx</sub>-F'(u), u<sub>x</sub>(0) = u<sub>x</sub>(1) = 0, </italic> where <italic> F(u) </italic> is a so-called \"double-well'' potential. We consider both classical and nonclassical examples for F. Furthermore, the main method we use in this discussion of stability is that of upper and lower solutions."],"dc:identifier.uri":["http://hdl.handle.net/10339/39323"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["analysis"],"dc:title":["On the Stability of Solutions to a Phase Transition Model"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:46Z"}