{"id":{"repo_id":"heid-diss","oai_identifier":"oai:archiv.ub.uni-heidelberg.de:4949"},"canonical_url":"https://search.dev.ndltd.org/etd/heid-diss/oai:archiv.ub.uni-heidelberg.de:4949","repository":{"repo_id":"heid-diss","name":"Universität Heidelberg","base_url":"http://archiv.ub.uni-heidelberg.de/volltextserver/cgi/oai2"},"display":{"title":"First-order geometric evolutions and semilinear evolution equations : a common mutational approach","abstract":"The primary aim of this Ph.D. thesis is to unify the definition of \"solution\" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.) Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces. Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).","abstract_html":"The primary aim of this Ph.D. thesis is to unify the definition of "solution" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.) Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces. Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).","abstract_has_math":false,"creators":["Lorenz, Thomas"],"institution":"Universität Heidelberg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Jäger, Willi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-09-28","date_published":"2004-09-28","updated_at":"2026-07-24T02:29:58Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://www.ub.uni-heidelberg.de/archiv/4949","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jäger, Willi"]},{"key":"dc:creator","label":"Author","values":["Lorenz, Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Heidelberg"]},{"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 Heidelberg"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The primary aim of this Ph.D. thesis is to unify the definition of \"solution\" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.) Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces. Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).","Das zentrale Ziel dieser Dissertation besteht in einem einheitlichen Lösungsbegriff für verschiedenartige Evolutionsprobleme. Er soll die Grundlage schaffen, um Systeme zu lösen, deren Komponenten ihren Ursprung in völlig unterschiedlichen Anwendungen finden. Als analytischer Prüfstein für den allgemeinen Charakter des Lösungsbegriffs wird ein System herangezogen, bestehend aus (1.) einer semilinearen Evolutionsgleichung in einem reflexiven Banachraum und (2.) einer geometrischen Evolution 1. Ordnung, d.h. einer zeitabhängigen kompakten Teilmenge des R^n, deren Deformation von nichtlokalen Eigenschaften ihrer Normalkegel am Rande abhängt. (Dabei soll kein Inklusionsprinzip verwendet werden.) Die Idee einer Ableitung als Approximation 1. Ordnung verlangt eine (verallgemeinerte) Abstandsfunktion. Sie ist im wesentlichen das einzige Mittel für einen abstrakten Ansatz außerhalb von Vektorräumen. Hier werden 2 Konzepte vorgestellt. Beide verallgemeinern die sog. Mutationsgleichungen von Jean-Pierre Aubin (in metrischen Räumen) auf Mengen mit einer abzählbaren Familie von sog. Scheinmetriken, die nicht mehr symmetrisch zu sein brauchen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["First-order geometric evolutions and semilinear evolution equations : a common mutational approach","Geometrische Evolutionen 1. Ordnung und semilineare Evolutionsgleichungen : ein gemeinsamer Ansatz durch Mutationen"]}]}],"canonical_facts":{"dc:contributor":["Jäger, Willi"],"dc:creator":["Lorenz, Thomas"],"dc:description.abstract":["The primary aim of this Ph.D. thesis is to unify the definition of \"solution\" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a reflexive Banach space and (2.) a first-order geometric evolution, i.e. a time-dependent compact subset of R^n, whose deformation depends on nonlocal properties of normal cones at the boundary. (No inclusion principle is assumed.) Taking up the widespread idea of derivatives as first-order approximations, distance functions (maybe in a generalized sense) are required and essentially the only tool to use for a general approach beyond vector spaces. Here two concepts are presented, both of which are based on generalizing the mutational equations of Jean-Pierre Aubin (in metric spaces) to a set with a countable family of so-called ostensible metrics (that need not be symmetric).","Das zentrale Ziel dieser Dissertation besteht in einem einheitlichen Lösungsbegriff für verschiedenartige Evolutionsprobleme. Er soll die Grundlage schaffen, um Systeme zu lösen, deren Komponenten ihren Ursprung in völlig unterschiedlichen Anwendungen finden. Als analytischer Prüfstein für den allgemeinen Charakter des Lösungsbegriffs wird ein System herangezogen, bestehend aus (1.) einer semilinearen Evolutionsgleichung in einem reflexiven Banachraum und (2.) einer geometrischen Evolution 1. Ordnung, d.h. einer zeitabhängigen kompakten Teilmenge des R^n, deren Deformation von nichtlokalen Eigenschaften ihrer Normalkegel am Rande abhängt. (Dabei soll kein Inklusionsprinzip verwendet werden.) Die Idee einer Ableitung als Approximation 1. Ordnung verlangt eine (verallgemeinerte) Abstandsfunktion. Sie ist im wesentlichen das einzige Mittel für einen abstrakten Ansatz außerhalb von Vektorräumen. Hier werden 2 Konzepte vorgestellt. Beide verallgemeinern die sog. Mutationsgleichungen von Jean-Pierre Aubin (in metrischen Räumen) auf Mengen mit einer abzählbaren Familie von sog. Scheinmetriken, die nicht mehr symmetrisch zu sein brauchen."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universitätsbibliothek Heidelberg"],"dc:title":["First-order geometric evolutions and semilinear evolution equations : a common mutational approach","Geometrische Evolutionen 1. Ordnung und semilineare Evolutionsgleichungen : ein gemeinsamer Ansatz durch Mutationen"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Heidelberg"]},"updated_at":"2026-07-24T02:29:58Z"}