@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-00855334v1> a dcat:Dataset ;
    dct:description """
              In this paper we are interested in the long time behaviour of the positive solutions of the mutation selection model with Neumann Boundary condition: $$ \\frac{\\partial u(x,t)}{dt}=u\\left[r(x)-\\int_{\\O}K(x,y)|u|^{p}(y)\\,dy\\right]+\\nabla\\cdot\\left(A(x)\\nabla u(x)\\right),\\qquad \\text{ in }\\quad \\R^+\\times\\O$$ where $\\O\\subset \\R^N$ is a bounded smooth domain, $k(.,.) \\in C(\\bar \\O \\times C(\\bar\\O), \\R), p\\ge 1$ and $A(x)$ is a smooth elliptic matrix. In a blind competition situation, i.e $K(x,y)=k(y)$, we show the existence of a unique positive steady state which is positively globally stable. That is, the positive steady state attracts all the possible trajectories initiated from any non negative initial datum. When $K$ is a general positive kernel, we also present a necessary and sufficient condition for the existence of a positive steady states. We prove also some stability result on the dynamic of the equation when the competition kernel $K$ is of the form $K(x,y)=k_0(y)+\\eps k_1(x,y)$. That is, we prove that for sufficiently small $\\eps$ there exists a unique steady state, which in addition is positively asymptotically stable. The proofs of the global stability of the steady state essentially rely on non-linear relative entropy identities and an orthogonal decomposition. These identities combined with the decomposition provide us some a priori estimates and differential inequalities essential to characterise the asymptotic behaviour of the solutions.
            """ ;
    dct:identifier "hal-00855334" ;
    dct:issued "2026-05-09T23:38:47.949492"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-09T23:38:47.949497"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Convergence to equilibrium for positive solutions of some mutation-selection model" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00855334v1/resource/fba9b2c0-b04a-443f-a8a3-a0eba4ef3f96> ;
    dcat:keyword "35r0935q9235b40",
        "asymptotic-behaviour",
        "equilibrium",
        "functional-inequality",
        "global-stability",
        "infoeu-reposemanticspreprint",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "preprints-working-papers-",
        "relative-entropy" ;
    dcat:landingPage <https://hal.science/hal-00855334> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00855334v1/resource/fba9b2c0-b04a-443f-a8a3-a0eba4ef3f96> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-09T23:38:47.951207"^^xsd:dateTime ;
    dct:modified "2026-05-09T23:38:47.939925"^^xsd:dateTime ;
    dct:title "Convergence to equilibrium for positive solutions of some mutation-selection model" ;
    dcat:accessURL <https://hal.science/hal-00855334> .

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

<https://hal.science/hal-00855334> a foaf:Document .