Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model

Bian, Shen; Chen, Li; Dreher, Michael

Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2012

Autor:innen

Bian, Shen

Chen, Li

Dreher, Michael

Publikationstyp

Zeitschriftenartikel

unikn.publication.listelement.citation.prefix.version.undefined

Journal of Differential Equations. 2012, 253(1), pp. 356-377. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2012.03.008

Zusammenfassung

We study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift–diffusion model of a semiconductor. We prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions. We prove analytical estimates of the remainder terms of this asymptotic expansion, and confirm by means of numerical simulations that these remainder estimates are sharp.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Quantum drift–diffusion model, Boundary layer, Elliptic system, Variational methods

Zitieren

ISO 690

BIAN, Shen, Li CHEN, Michael DREHER, 2012. Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model. In: Journal of Differential Equations. 2012, 253(1), pp. 356-377. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2012.03.008

BibTex

@article{Bian2012Bound-22045,
  year={2012},
  doi={10.1016/j.jde.2012.03.008},
  title={Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model},
  number={1},
  volume={253},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={356--377},
  author={Bian, Shen and Chen, Li and Dreher, Michael}
}

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/123456789/22045">
    <dcterms:issued>2012</dcterms:issued>
    <dc:language>eng</dc:language>
    <dc:contributor>Chen, Li</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:title>Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model</dcterms:title>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-02-22T14:44:29Z</dcterms:available>
    <dc:contributor>Bian, Shen</dc:contributor>
    <dc:creator>Bian, Shen</dc:creator>
    <dc:rights>terms-of-use</dc:rights>
    <dcterms:abstract xml:lang="eng">We study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift–diffusion model of a semiconductor. We prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions. We prove analytical estimates of the remainder terms of this asymptotic expansion, and confirm by means of numerical simulations that these remainder estimates are sharp.</dcterms:abstract>
    <dc:creator>Dreher, Michael</dc:creator>
    <dcterms:bibliographicCitation>Journal of Differential Equations ; 253 (2012), 1. - S. 356-377</dcterms:bibliographicCitation>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Dreher, Michael</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/22045"/>
    <dc:creator>Chen, Li</dc:creator>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-02-22T14:44:29Z</dc:date>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja