title: Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms
creator: Lorenz, Thomas
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 2007
type: Preprint
type: info:eu-repo/semantics/preprint
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/7392/1/Lorenz_mutational_equations_revised.pdf
identifier: DOI:10.11588/heidok.00007392
identifier: urn:nbn:de:bsz:16-opus-73928
identifier:   Lorenz, Thomas  (2007) Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms.  [Preprint]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/7392/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng