eprintid: 5993 rev_number: 12 eprint_status: archive userid: 1 dir: disk0/00/00/59/93 datestamp: 2005-01-22 13:55:10 lastmod: 2015-04-22 04:46:23 status_changed: 2012-08-14 15:16:51 type: preprint metadata_visibility: show creators_name: Lorenz, Thomas title: Quasilinear continuity equations of measures for bounded BV vector fields ispublished: pub subjects: 510 divisions: 708000 keywords: conservative continuity equation , measure-valued distributional solution , generalized ODE on sets with nonsymmetric distances , mutational equations cterms_swd: Kontinuitätsgleichung cterms_swd: Quasilineare partielle Differentialgleichung cterms_swd: Maß cterms_swd: Distribution abstract: The focus of interest here is a quasilinear form of the conservative continuity equation d/dt v + D·(f(v, ·) v) = 0 (in R^N× ]0, T[) together with its measure-valued distributional solutions. On the basis of Ambrosio’s results about the nonautonomous linear equation, the existence and uniqueness of solutions are investigated for coefficients being bounded vector fields with bounded spatial variation and Lebesgue absolutely continuous divergence in combination with positive measures absolutely continuous with respect to Lebesgue measure. The step towards the nonlinear problem here relies on a further generalization of Aubin's mutational equations that is extending the notions of distribution-like solutions and "weak compactness" to a set supplied with a countable family of (possibly non–symmetric) distance functions (so–called ostensible metrics). abstract_translated_lang: eng class_scheme: msc class_labels: 49J52, 34G20, 26B30, 35F25 date: 2005 date_type: published id_scheme: DOI id_number: 10.11588/heidok.00005993 portal_cluster_id: p-iwrpp portal_order: 05993 ppn_swb: 1646175417 own_urn: urn:nbn:de:bsz:16-heidok-59939 language: eng bibsort: LORENZTHOMQUASILINEA2005 full_text_status: public series: IWR-Preprints citation: Lorenz, Thomas (2005) Quasilinear continuity equations of measures for bounded BV vector fields. [Preprint] document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/5993/1/Lorenz_quasilin_continuity_equation_revised.pdf document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/5993/2/Lorenz_quasilin_continuity_equation_revised.pdf.old