@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00951543v1> a dcat:Dataset ;
    dct:description """
              In this paper we are interested in the convergence of accumulation of dislocations to walls of dislocations. We consider the dynamical system generated by the force $f(x,y)=\\frac{x(y^{2}-x^{2})}{(y^{2}+x^{2})^{2}}$, defined over $\\R\\times\\Z\\backslash\\{0\\},$ that describes the phenomena. For initial data $X^{0}\\in\\Omega\\cap\\ell^{\\infty}=\\left\\{X: |x_{i} - x_{j}| \\leqslant \\sqrt{3 - 2\\sqrt{2}} \\,|i-j| \\right\\}\\cap\\ell^{\\infty},$ we show %% using Cauchy Lipschitz theorem the existence of unique solution $X\\in C^{1}\\in([0,+\\infty),\\Omega\\cap\\ell^{\\infty}).$ Moreover, we prove that if $X^{0}$ is periodic, then $X(t)=(x_{j}(t))_{j\\in\\Z}$ is periodic for any $t>0$ and converges to the barycenter of the initial data, i.e. $x_{j}(t)\\to c=\\frac{1}{N}\\sum_{i=1}^{N}x_{i}^{0}$ for every $j\\in\\Z.$ We also establish a $\\ell^{p}$ contraction for periodic solutions and perform numerical simulations.
            """ ;
    dct:identifier "hal-00951543" ;
    dct:issued "2026-05-06T06:15:26.389909"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-06T06:15:26.389913"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Convergence to walls of dislocations in the periodic case" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00951543v1/resource/9e3faf4a-7503-4f47-a40c-509745244ebf> ;
    dcat:keyword "cauchy-lipschitz-theorem",
        "comparison-principle",
        "dynamical-system",
        "infoeu-reposemanticspreprint",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "periodic-solution",
        "preprints-working-papers-",
        "viscosity-solutions" ;
    dcat:landingPage <https://hal.science/hal-00951543> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00951543v1/resource/9e3faf4a-7503-4f47-a40c-509745244ebf> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-06T06:15:26.404830"^^xsd:dateTime ;
    dct:modified "2026-05-06T06:15:26.373283"^^xsd:dateTime ;
    dct:title "Convergence to walls of dislocations in the periodic case" ;
    dcat:accessURL <https://hal.science/hal-00951543> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://hal.science/hal-00951543> a foaf:Document .