eprintid: 5519
rev_number: 8
eprint_status: archive
userid: 1
dir: disk0/00/00/55/19
datestamp: 2005-05-18 13:55:45
lastmod: 2015-04-22 17:20:42
status_changed: 2012-08-14 15:15:01
type: preprint
metadata_visibility: show
creators_name: Lorenz, Thomas
title: Evolution equations in ostensible metric spaces : Definitions and existence.
ispublished: pub
subjects: 510
divisions: 708000
keywords: Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von Differentialinklusionengeneralized ODE on sets with nonsymmetric distance functions , nonlocal geometric evolutions , mutational equations , set-valued maps
cterms_swd: Verallgemeinerte Differentialgleichung
cterms_swd: Nichtlineare Evolutionsgleichung
cterms_swd: Nichtglatte Analysis
cterms_swd: Mengenwertige Abbildung
cterms_swd: Stark stetige Halbgruppe
abstract: The primary aim 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 like, for example, a semilinear evolution equation (of parabolic type) in combination with a first order geometric evolution. In regard to geometric evolutions, this concept is to fulfill 3 conditions : First, consider nonempty compact subsets K(t) of R^N without a priori restrictions on the regularity of the boundary. Second, the evolution of K(t) might depend on nonlocal properties of the set K(t) and its normal cones. Last, but not least, no inclusion principle.  The approach here is based on generalizing the mutational equations of Aubin for metric spaces in two respects : Replacing the metric by a countable family of (possibly nonsymmetric) distances (called ostensible metrics) and extending the basic idea of distributions.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 47D06, 34G25, 34A60, 34G20, 49J53
date: 2005
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00005519
portal_cluster_id: p-iwrpp
portal_order: 05519
ppn_swb: 164617478X
own_urn: urn:nbn:de:bsz:16-heidok-55194
language: eng
bibsort: LORENZTHOMEVOLUTIONE2005
full_text_status: public
series: IWR-Preprints
citation:   Lorenz, Thomas  (2005) Evolution equations in ostensible metric spaces : Definitions and existence.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/5519/1/Lorenz_ostensible_metric.pdf