eprintid: 6777
rev_number: 13
eprint_status: archive
userid: 1
dir: disk0/00/00/67/77
datestamp: 2006-08-11 07:12:36
lastmod: 2015-04-24 04:26:07
status_changed: 2012-08-14 15:19:25
type: preprint
metadata_visibility: show
creators_name: Lorenz, Thomas
title: A viability theorem for morphological inclusions
ispublished: pub
subjects: ddc-510
divisions: i-708000
keywords: Shape evolutions with constraints , velocity method (speed method) , morphological equations , Nagumo's theorem , viability condition
cterms_swd: Verallgemeinerte Differentialgleichung
cterms_swd: Kompakte Menge
cterms_swd: Mengenwertige Abbildung
cterms_swd: Nebenbedingung
abstract: The aim of this paper is to adapt the Viability Theorem from differential inclusions (governing the evolution of vectors in a finite dimensional space) to so-called morphological inclusions (governing the evolution of nonempty compact subsets of the Euclidean space). In this morphological framework, the evolution of compact subsets of the Euclidean space is described by means of flows along bounded Lipschitz vector fields (similarly to the velocity method alias speed method in shape analysis). Now for each compact subset, more than just one vector field is admitted - correspondingly to the set-valued map of a differential inclusion in finite dimensions. We specify sufficient conditions on the given data such that for every initial compact set, at least one of these compact-valued evolutions satisfies fixed state constraints in addition. The proofs follow an approximative track similar to the standard approach for differential inclusions in finite dimensions, but they use tools about weak compactness and weak convergence of Banach-valued functions. Finally an application to shape optimization under state constraints is sketched.
abstract_translated_lang: eng
class_scheme: msc
class_labels: 93C15, 49J24, 49Q10, 49J53, 34A60
date: 2006
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00006777
portal_cluster_id: p-iwrpp
portal_order: 06777
ppn_swb: 1646175433
own_urn: urn:nbn:de:bsz:16-opus-67773
language: eng
bibsort: LORENZTHOMAVIABILITY2006
full_text_status: public
series: IWR-Preprints
citation:   Lorenz, Thomas  (2006) A viability theorem for morphological inclusions.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/6777/1/Lorenz_morphological_viability_theorem_SIAM.pdf
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/6777/2/Lorenz_shape_viability_theorem.pdf.old