Publikation:

Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology

Vorschaubild

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2007

Autor:innen

Gerisch, Alf
Zacher, Rico

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

URI (zitierfähiger Link)
http://nbn-resolving.de/urn:nbn:de:bsz:352-254969
DOI (zitierfähiger Link)
https://doi.org/10.1007/s00030-007-5023-2
ArXiv-ID

Internationale Patentnummer

Angaben zur Forschungsförderung

Projekt

Open Access-Veröffentlichung

Sammlungen

Mathematik und Statistik: Publikationen
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published

Erschienen in

Nonlinear Differential Equations and Applications NoDEA. 2007, 14(5-6), pp. 593-624. ISSN 1021-9722. eISSN 1420-9004. Available under: doi: 10.1007/s00030-007-5023-2

Zusammenfassung

We study the existence of classical solutions of a taxis-diffusion-reaction model for tumour-induced blood vessel growth. The model in its basic form has been proposed by Chaplain and Stuart (IMA J. Appl. Med. Biol. (10), 1993) and consists of one equation for the endothelial cell-density and another one for the concentration of tumour angiogenesis factor (TAF). Here we consider the special and interesting case that endothelial cells are immobile in the absence of TAF, i.e. vanishing cell motility. In this case the mathematical structure of the model changes significantly (from parabolic type to a mixed hyperbolic-parabolic type) and existence of solutions is by no means clear. We present conditions on the initial and boundary data which guarantee local existence, uniqueness and positivity of classical solutions of the problem. Our approach is based on the method of characteristics and relies on known maximal L p and Hölder regularity results for the diffusion equation.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690GERISCH, Alf, Matthias KOTSCHOTE, Rico ZACHER, 2007. Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology. In: Nonlinear Differential Equations and Applications NoDEA. 2007, 14(5-6), pp. 593-624. ISSN 1021-9722. eISSN 1420-9004. Available under: doi: 10.1007/s00030-007-5023-2
BibTex
@article{Gerisch2007Wellp-25496,
  year={2007},
  doi={10.1007/s00030-007-5023-2},
  title={Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology},
  number={5-6},
  volume={14},
  issn={1021-9722},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  pages={593--624},
  author={Gerisch, Alf and Kotschote, Matthias and Zacher, Rico}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/25496">
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-12-18T08:13:07Z</dc:date>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/25496"/>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:bibliographicCitation>Nonlinear Differential Equations and Applications ; 14 (2007), 5-6. - S. 593-624</dcterms:bibliographicCitation>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:title>Well-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology</dcterms:title>
    <dc:language>eng</dc:language>
    <dcterms:issued>2007</dcterms:issued>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Gerisch, Alf</dc:creator>
    <dc:creator>Zacher, Rico</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-12-18T08:13:07Z</dcterms:available>
    <dc:creator>Kotschote, Matthias</dc:creator>
    <dc:contributor>Kotschote, Matthias</dc:contributor>
    <dcterms:abstract xml:lang="eng">We study the existence of classical solutions of a taxis-diffusion-reaction model for tumour-induced blood vessel growth. The model in its basic form has been proposed by Chaplain and Stuart (IMA J. Appl. Med. Biol. (10), 1993) and consists of one equation for the endothelial cell-density and another one for the concentration of tumour angiogenesis factor (TAF). Here we consider the special and interesting case that endothelial cells are immobile in the absence of TAF, i.e. vanishing cell motility. In this case the mathematical structure of the model changes significantly (from parabolic type to a mixed hyperbolic-parabolic type) and existence of solutions is by no means clear. We present conditions on the initial and boundary data which guarantee local existence, uniqueness and positivity of classical solutions of the problem. Our approach is based on the method of characteristics and relies on known maximal L p and Hölder regularity results for the diffusion equation.</dcterms:abstract>
    <dc:contributor>Zacher, Rico</dc:contributor>
    <dc:contributor>Gerisch, Alf</dc:contributor>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Nein
Begutachtet
Diese Publikation teilen