eprintid: 8966
rev_number: 12
eprint_status: archive
userid: 1
dir: disk0/00/00/89/66
datestamp: 2009-01-21 09:24:11
lastmod: 2014-04-03 21:04:27
status_changed: 2012-08-14 15:27:40
type: doctoralThesis.habil
metadata_visibility: show
creators_name: Lorenz, Thomas
title: Mutational Analysis
ispublished: pub
subjects: 510
divisions: 708000
adv_faculty: af-11
keywords: Mutationsgleichungen , nichtsymmetrische Abstandsfunktionen , nichtlokale geometrische Evolutionen , erreichbare Mengen von Differentialinklusionen
cterms_swd: Verallgemeinerte Differentialgleichung
cterms_swd: Nichtlineare Evolutionsgleichung
cterms_swd: Nichtglatte Analysis
cterms_swd: Mengenwertige Abbildung
abstract: This monograph extends the classical concept of ordinary differential equations in the Euclidean space to nonempty sets which are just supplied with a family of "continuous" distance functions. In particular, these sets are not supposed to have any linear structure or to be metric spaces. The main goal is a joint framework for continuous dynamical systems beyond the traditional border of vector spaces so that examples of completely different origins can be coupled in systems. It is motivated by the mutational equations introduced by Jean-Pierre Aubin in the 1990s. Some of the examples discussed here are: nonlocal set evolutions, semilinear evolution equations, nonlinear transport equations for finite Radon measures, functional stochastic differential equations, parabolic differential equations in noncylindrical domains. This monograph is my revised Habilitationsschrift (i.e. thesis for a postdoctoral lecture qualification in Germany) submitted to the Faculty of Mathematics and Computer Science at Heidelberg University in January 2009. 
abstract_translated_lang: eng
class_scheme: msc
class_labels: 49J53, 34G25, 49-02, 93C15, 34A60
date: 2009
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00008966
ppn_swb: 606114505
own_urn: urn:nbn:de:bsz:16-opus-89660
date_accepted: 2009-07-01
advisor: HASH(0x5561209f6378)
language: eng
bibsort: LORENZTHOMMUTATIONAL2009
full_text_status: public
citation:   Lorenz, Thomas  (2009) Mutational Analysis.  [Habilitation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/8966/1/Lorenz_Mutational_Analysis.pdf
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/8966/2/Lorenz__Mutational_Analysis.pdf.old