{"id":{"repo_id":"qucosa-diss","oai_identifier":"oai:qucosa:de:qucosa:24821"},"canonical_url":"https://search.dev.ndltd.org/etd/qucosa-diss/oai:qucosa:de:qucosa:24821","repository":{"repo_id":"qucosa-diss","name":"QUCOSA","base_url":"http://www.qucosa.de/oai/"},"display":{"title":"Well-posedness and causality for a class of evolutionary inclusions","abstract":"We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations.","abstract_html":"We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations.","abstract_has_math":false,"creators":["Trostorff, Sascha"],"institution":"Technische Universität Dresden","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Picard, Rainer","Milani, Albert"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-10-25","date_published":"2011-10-25","updated_at":"2026-07-24T03:58:35Z","subjects":["Partielle Differentialgleichungen","Monotone Operatoren","Differentialinklusionen","Evolutionäre Gleichungen","Partial differential equations","monotone operators","differential inclusions","evolutionary equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Picard, Rainer","Milani, Albert"]},{"key":"dc:creator","label":"Author","values":["Trostorff, Sascha"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Technische Universität Dresden"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Partielle Differentialgleichungen","Monotone Operatoren","Differentialinklusionen","Evolutionäre Gleichungen","Partial differential equations","monotone operators","differential inclusions","evolutionary equations"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations."]},{"key":"dc:title","label":"Title","values":["Well-posedness and causality for a class of evolutionary inclusions"]}]}],"canonical_facts":{"dc:contributor":["Picard, Rainer","Milani, Albert"],"dc:creator":["Trostorff, Sascha"],"dc:description.abstract":["We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations."],"dc:publisher":["Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden"],"dc:subject":["Partielle Differentialgleichungen","Monotone Operatoren","Differentialinklusionen","Evolutionäre Gleichungen","Partial differential equations","monotone operators","differential inclusions","evolutionary equations"],"dc:title":["Well-posedness and causality for a class of evolutionary inclusions"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Technische Universität Dresden"]},"updated_at":"2026-07-24T03:58:35Z"}