title: First-order geometric evolutions and semilinear evolution equations : a common mutational approach
creator: Lorenz, Thomas
subject: ddc-510
subject: 510 Mathematics
description: 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).
date: 2004
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/4949/1/lorenz_dissertation.pdf
identifier: DOI:10.11588/heidok.00004949
identifier: urn:nbn:de:bsz:16-opus-49499
identifier:   Lorenz, Thomas  (2004) First-order geometric evolutions and semilinear evolution equations : a common mutational approach.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/4949/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng