Nonlocal-to-Local Convergence of Cahn–Hilliard Equations : Neumann Boundary Conditions and Viscosity Terms

Davoli, Elisa; Scarpa, Luca; Trussardi, Lara

Nonlocal-to-Local Convergence of Cahn–Hilliard Equations : Neumann Boundary Conditions and Viscosity Terms

Dateien

Davoli_2-1lc36jau2d9mh9.pdfGröße: 472.3 KBDownloads: 143

Datum

2021

Autor:innen

Davoli, Elisa

Scarpa, Luca

Trussardi, Lara

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Archive for Rational Mechanics and Analysis. Springer. 2021, 239(1), pp. 117-149. ISSN 0003-9527. eISSN 1432-0673. Available under: doi: 10.1007/s00205-020-01573-9

Zusammenfassung

We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.g. of logarithmic type), while the singularity of the convolution kernel does not fall in any available existence theory under Neumann boundary conditions. We prove well-posedness for the nonlocal equation in a suitable variational sense. Secondly, we show that the solutions to the nonlocal equation converge to the corresponding solutions to the local equation, as the convolution kernels approximate a Dirac delta. The asymptotic behaviour is analyzed by means of monotone analysis and Gamma convergence results, both when the limiting local Cahn-Hilliard equation is of viscous type and of pure type.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

DAVOLI, Elisa, Luca SCARPA, Lara TRUSSARDI, 2021. Nonlocal-to-Local Convergence of Cahn–Hilliard Equations : Neumann Boundary Conditions and Viscosity Terms. In: Archive for Rational Mechanics and Analysis. Springer. 2021, 239(1), pp. 117-149. ISSN 0003-9527. eISSN 1432-0673. Available under: doi: 10.1007/s00205-020-01573-9

BibTex

@article{Davoli2021Nonlo-55533,
  year={2021},
  doi={10.1007/s00205-020-01573-9},
  title={Nonlocal-to-Local Convergence of Cahn–Hilliard Equations : Neumann Boundary Conditions and Viscosity Terms},
  number={1},
  volume={239},
  issn={0003-9527},
  journal={Archive for Rational Mechanics and Analysis},
  pages={117--149},
  author={Davoli, Elisa and Scarpa, Luca and Trussardi, Lara}
}

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/123456789/55533">
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55533/1/Davoli_2-1lc36jau2d9mh9.pdf"/>
    <dc:rights>Attribution 4.0 International</dc:rights>
    <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">2021-11-12T12:57:28Z</dc:date>
    <dc:creator>Trussardi, Lara</dc:creator>
    <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-11-12T12:57:28Z</dcterms:available>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/55533/1/Davoli_2-1lc36jau2d9mh9.pdf"/>
    <dcterms:issued>2021</dcterms:issued>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/55533"/>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:contributor>Scarpa, Luca</dc:contributor>
    <dc:contributor>Trussardi, Lara</dc:contributor>
    <dcterms:title>Nonlocal-to-Local Convergence of Cahn–Hilliard Equations : Neumann Boundary Conditions and Viscosity Terms</dcterms:title>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Davoli, Elisa</dc:contributor>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Davoli, Elisa</dc:creator>
    <dc:creator>Scarpa, Luca</dc:creator>
    <dcterms:abstract xml:lang="eng">We consider a class of nonlocal viscous Cahn-Hilliard equations with Neumann boundary conditions for the chemical potential. The double-well potential is allowed to be singular (e.g. of logarithmic type), while the singularity of the convolution kernel does not fall in any available existence theory under Neumann boundary conditions. We prove well-posedness for the nonlocal equation in a suitable variational sense. Secondly, we show that the solutions to the nonlocal equation converge to the corresponding solutions to the local equation, as the convolution kernels approximate a Dirac delta. The asymptotic behaviour is analyzed by means of monotone analysis and Gamma convergence results, both when the limiting local Cahn-Hilliard equation is of viscous type and of pure type.</dcterms:abstract>
    <dc:language>eng</dc:language>
  </rdf:Description>
</rdf:RDF>

Universitätsbibliographie

Ja

Begutachtet

Unbekannt