eprintid: 7392
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/73/92
datestamp: 2007-06-05 14:46:00
lastmod: 2015-04-28 13:10:55
status_changed: 2012-08-14 15:21:47
type: preprint
metadata_visibility: show
creators_name: Lorenz, Thomas
title: Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
ispublished: pub
subjects: ddc-510
divisions: i-708000
keywords: Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von DifferentialinklusionenMutational equations , quasidifferential equations , nonlocal geometric evolutions, reachable sets of differential inclusions , sets of positive reach
cterms_swd: Verallgemeinerte Differentialgleichung
cterms_swd: Nichtlineare Evolutionsgleichung
cterms_swd: Nichtglatte Analysis
cterms_swd: Mengenwertige Abbildung
abstract: Similarly to funnel equations of Panasyuk, the so-called mutational equations of Aubin provide a generalization of ordinary differential equations to locally compact metric spaces. Here we present their extension to a nonempty set with a possibly nonsymmetric distance. A distribution-like approach leads to so-called right-hand forward solutions. This concept is applied to a type of geometric evolution having motivated the definitions : compact subsets of the Euclidean space evolve according to nonlocal properties of both the set and their limiting normal cones at the boundary. The existence of a solution is based on Euler method using reachable sets of differential inclusions as "elementary deformations" (called forward transitions). Thus, the regularity of these reachable sets at the topological boundaries is studied extensively in the appendix.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 47D06, 34G25, 34A60, 49J53, 34G20
date: 2007
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00007392
ppn_swb: 1646175808
own_urn: urn:nbn:de:bsz:16-opus-73928
language: eng
bibsort: LORENZTHOMEVOLUTIONE2007
full_text_status: public
citation:   Lorenz, Thomas  (2007) Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/7392/1/Lorenz_mutational_equations_revised.pdf