{"id":{"repo_id":"potsdam-diss","oai_identifier":"oai:kobv.de-opus4-uni-potsdam:1561"},"canonical_url":"https://search.dev.ndltd.org/etd/potsdam-diss/oai:kobv.de-opus4-uni-potsdam:1561","repository":{"repo_id":"potsdam-diss","name":"Universität Potsdam - Diss","base_url":"https://publishup.uni-potsdam.de/opus4-ubp/oai"},"display":{"title":"The evolution equation for closed magnetic geodesics","abstract":"Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a \"generalized physical force\". For the corresponding evolution equation, which is a system of parabolic nonlinear partial differential equations associated to the elliptic PDE, we can establish existence of short time solutions.","abstract_html":"Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a "generalized physical force". For the corresponding evolution equation, which is a system of parabolic nonlinear partial differential equations associated to the elliptic PDE, we can establish existence of short time solutions.","abstract_has_math":false,"creators":["Koh, Dennis"],"institution":"Universität Potsdam","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bär, Christian"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-02-27","date_published":"2008-02-27","updated_at":"2026-07-24T03:51:24Z","subjects":["magnetisch","Geodäten","Evolutionsgleichung","Strings","p-Branen","magnetic","geodesics","evolution equation","p-branes"],"languages":[],"rights":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 2.0 Deutschland"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1561","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bär, Christian"]},{"key":"dc:creator","label":"Author","values":["Koh, Dennis"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universität Potsdam"]},{"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":["Universität Potsdam"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["magnetisch","Geodäten","Evolutionsgleichung","Strings","p-Branen","magnetic","geodesics","evolution equation","p-branes"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 2.0 Deutschland"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a \"generalized physical force\". For the corresponding evolution equation, which is a system of parabolic nonlinear partial differential equations associated to the elliptic PDE, we can establish existence of short time solutions.","Bahnen von geladenen Teilchen, die sich unter dem Einfluss eines Magnetfeldes bewegen, werden in der Mathematik durch magnetische Geodäten beschrieben. Sie ergeben sich als Lösungen eines Systems (nichtlinearer) gewöhnlicher Differentialgleichungen zweiter Ordnung. Wir interessieren uns ausschließich für periodische Lösungen. Dazu studieren wir das zugehörige System (nichtlinearer) parabolischer Differentialgleichungen für geschlossene magnetische Geodäten. Als Hauptresultat beweisen wir die Existenz von Langzeitlösungen. Verallgemeinernd betrachten wir noch ein System von elliptischen nichtlinearen partiellen Differentialgleichungen, dessen Lösungen die Orbiten von geschlossenen p-Branen unter dem Einfluss einer verallgemeinerten physikalischen Kraft beschreiben. Für die entsprechende Evolutionsgleichung, welche ein System von parabolischen nichtlinearen partiellen Differentialgleichungen ist, das dem elliptischen Problem zugeordnet ist, können wir die Existenz von Kurzzeitlösungen beweisen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The evolution equation for closed magnetic geodesics","Die Evolutionsgleichung für geschlossene magnetische Geodäten"]}]}],"canonical_facts":{"dc:contributor":["Bär, Christian"],"dc:creator":["Koh, Dennis"],"dc:description.abstract":["Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a \"generalized physical force\". For the corresponding evolution equation, which is a system of parabolic nonlinear partial differential equations associated to the elliptic PDE, we can establish existence of short time solutions.","Bahnen von geladenen Teilchen, die sich unter dem Einfluss eines Magnetfeldes bewegen, werden in der Mathematik durch magnetische Geodäten beschrieben. Sie ergeben sich als Lösungen eines Systems (nichtlinearer) gewöhnlicher Differentialgleichungen zweiter Ordnung. Wir interessieren uns ausschließich für periodische Lösungen. Dazu studieren wir das zugehörige System (nichtlinearer) parabolischer Differentialgleichungen für geschlossene magnetische Geodäten. Als Hauptresultat beweisen wir die Existenz von Langzeitlösungen. Verallgemeinernd betrachten wir noch ein System von elliptischen nichtlinearen partiellen Differentialgleichungen, dessen Lösungen die Orbiten von geschlossenen p-Branen unter dem Einfluss einer verallgemeinerten physikalischen Kraft beschreiben. Für die entsprechende Evolutionsgleichung, welche ein System von parabolischen nichtlinearen partiellen Differentialgleichungen ist, das dem elliptischen Problem zugeordnet ist, können wir die Existenz von Kurzzeitlösungen beweisen."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universität Potsdam"],"dc:rights":["Creative Commons - Namensnennung, Nicht kommerziell, Weitergabe zu gleichen Bedingungen 2.0 Deutschland"],"dc:subject":["magnetisch","Geodäten","Evolutionsgleichung","Strings","p-Branen","magnetic","geodesics","evolution equation","p-branes"],"dc:title":["The evolution equation for closed magnetic geodesics","Die Evolutionsgleichung für geschlossene magnetische Geodäten"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Potsdam"]},"updated_at":"2026-07-24T03:51:24Z"}