@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#> .

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    dct:description """
              We prove that the Cauchy problem associated with the one dimensional quadratic (fractional) heat equation: $u_t=D_x^{2\\alpha} u \\mp u^2,\\; t\\in (0,T),\\; x\\in \\R$ or $ \\T $, with $ 0<\\alpha\\le 1 $ is well-posed in $ H^s $ for $ s\\ge \\max(-\\alpha,1/2-2\\alpha) $ except in the case $ \\alpha=1/2 $ where it is shown to be well-posed for $ s>-1/2 $ and ill-posed for $ s=-1/2 $. As a by-product we improve the known well-posedness results for the heat equation ($\\alpha=1$) by reaching the end-point Sobolev index $ s=-1 $. Finally, in the case $ 1/2<\\alpha\\le 1 $, we also prove optimal results in the Besov spaces $B^{s,q}_2.$
            """ ;
    dct:identifier "hal-00807047" ;
    dct:issued "2026-05-11T17:35:38.043669"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-11T17:35:38.043674"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Remarks on the Cauchy problem for the one-dimensional quadratic (fractional) heat equation" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00807047v1/resource/d5c6c035-005a-4613-8761-ca54244f36f0> ;
    dcat:keyword "35k15-35k55-35k65-35b40",
        "besov-spaces",
        "fractional-heat-equation",
        "ill-posedness",
        "infoeu-reposemanticsarticle",
        "journal-articles",
        "mathmath-apmathematics-mathanalysis-of-pdes-mathap",
        "nonlinear-heat-equation",
        "sobolev-spaces",
        "well-posedness" ;
    dcat:landingPage <ISSN:%200022-1236> .

<ISSN:%200022-1236> a foaf:Document .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00807047v1/resource/d5c6c035-005a-4613-8761-ca54244f36f0> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-11T17:35:38.065846"^^xsd:dateTime ;
    dct:modified "2026-05-11T17:35:38.029921"^^xsd:dateTime ;
    dct:title "Remarks on the Cauchy problem for the one-dimensional quadratic (fractional) heat equation" ;
    dcat:accessURL <https://hal.science/hal-00807047> .

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