eprintid: 7252
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/72/52
datestamp: 2007-02-28 13:08:50
lastmod: 2015-04-21 23:50:56
status_changed: 2012-08-14 15:21:09
type: preprint
metadata_visibility: show
creators_name: Lorenz, Thomas
title: Radon measures solving the Cauchy problem of the nonlinear transport equation
ispublished: pub
subjects: ddc-510
divisions: i-708000
keywords: nonlinear transport equation , Radon measures on Euclidean space with compact support , mutational equations in metric space
cterms_swd: Transportgleichung
cterms_swd: Nichtlineare partielle Differentialgleichung
cterms_swd: Radon-Maß
cterms_swd: Verallgemeinerte Differentialgleichung
abstract: The focus of interest is the Cauchy problem of the nonlinear transport equation d_t u + div (f(u, ·) u) = g(u, ·) u together with its distributional solutions u(·) whose values are positive Radon measures on the Euclidean space with compact support. The coefficients f(u, t), g(u, t) are assumed to be uniformly bounded and Lipschitz continuous vector fields on the Euclidean space. Sufficient conditions on the coefficients for existence, uniqueness and even for stability of these distributional solutions are presented. Starting from the well-known results about the corresponding linear problem, the step towards the nonlinear problem here relies on Aubin's mutational equations, i.e. dynamical systems in a metric space (with a new slight modification).
abstract_translated_lang: eng
class_scheme: msc
class_labels: 35L60, 35F25, 28A33, 34G20, 82C70
date: 2007
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00007252
portal_cluster_id: p-iwrpp
portal_order: 07252
ppn_swb: 1646175573
own_urn: urn:nbn:de:bsz:16-opus-72527
language: ger
bibsort: LORENZTHOMRADONMEASU2007
full_text_status: public
series: IWR-Preprints
citation:   Lorenz, Thomas  (2007) Radon measures solving the Cauchy problem of the nonlinear transport equation.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/7252/1/Lorenz_nonlinear_transport_equation.pdf