@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-00694470v1> a dcat:Dataset ;
    dct:description """
              We consider the stochastic CGL equation $$ \\dot u- \\nu\\Delta u+(i+a) |u|^2u =\\eta(t,x),\\;\\;\\; \\text {dim} \\,x=n, $$ where $\\nu>0$ and $a\\ge 0$, in a cube (or in a smooth bounded domain) with Dirichlet boundary condition. The force $\\eta$ is white in time, regular in $x$ and non-degenerate. We study this equation in the space of continuous complex functions $u(x)$, and prove that for any $n$ it defines there a unique mixing Markov process. So for a large class of functionals $f(u(\\cdot))$ and for any solution $u(t,x)$, the averaged observable $\\E f(u(t,\\cdot))$ converges to a quantity, independent from the initial data $u(0,x)$, and equal to the integral of $f(u)$ against the unique stationary measure of the equation.
            """ ;
    dct:identifier "hal-00694470" ;
    dct:issued "2026-05-19T21:39:09.028831"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-19T21:39:09.028837"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Stochastic CGL equations without linear dispersion in any space dimension" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00694470v1/resource/77aaef70-cf38-49c9-b207-6fdca80fc863> ;
    dcat:keyword "infoeu-reposemanticspreprint",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "preprints-working-papers-" ;
    dcat:landingPage <https://hal.science/hal-00694470> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00694470v1/resource/77aaef70-cf38-49c9-b207-6fdca80fc863> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-19T21:39:09.060972"^^xsd:dateTime ;
    dct:modified "2026-05-19T21:39:09.017234"^^xsd:dateTime ;
    dct:title "Stochastic CGL equations without linear dispersion in any space dimension" ;
    dcat:accessURL <https://hal.science/hal-00694470> .

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

<https://hal.science/hal-00694470> a foaf:Document .