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Parabolic equations with natural growth approximated by nonlocal equations

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dc.contributor.authorLeonori, Tommaso
dc.contributor.authorMolino, Alexis
dc.contributor.authorSegura De León, Sergio
dc.contributor.orcidhttps://orcid.org/0000-0002-0848-4463
dc.contributor.orcidhttps://orcid.org/0000-0003-2819-7282
dc.contributor.orcidhttps://orcid.org/0000-0002-8515-7108
dc.date.accessioned2024-11-20T07:18:40Z
dc.date.available2024-11-20T07:18:40Z
dc.date.issued2021
dc.description.abstracten
dc.description.abstractIn this paper, we study several aspects related with solutions of nonlocal problems whose prototype is {u(t) = integral N-R J (x - y)(u(y, t) u( x, t))g (u(y , t) u( x, t))dy in Omega x (0, T), u(x, 0) = u(0)(x) in Omega, where we take, as the most important instance, g(s) similar to 1 + mu/2 s/1+mu(2)s(2) with mu is an element of R as well as mu(0)is an element of L-1 (Omega), J is a smooth symmetric function with compact support and S2 is either a bounded smooth subset of R-N, with nonlocal Dirichlet boundary condition, or RN itself. The results deal with existence, uniqueness, comparison principle and asymptotic behavior. Moreover, we prove that if the kernel is resealed in a suitable way, the unique solution of the above problem converges to a solution of the deterministic Kardar Parisi Zhang equation.
dc.description.versionversión final
dc.identifier.citationLeonori, T., Molino, A., Segura De León, S. ; Parabolic equations with natural growth approximated by nonlocal equations (2021) Communications in Contemporary Mathematics, 23 (1), art. no. 1950088. : http://doi.org/10.1142/S0219199719500883
dc.identifier.doihttps://doi.org/10.1142/S0219199719500883
dc.identifier.issn0219-1997; e-ISSN: 1793-6683
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24435
dc.journal.issue1
dc.journal.titleCommunications in Contemporary Mathematics
dc.journal.volume23
dc.language.isoen
dc.publisherWorld Scientific
dc.relation.centerFacultades y escuelas::Facultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsNonlocal problemsen
dc.subject.keywordsKPZ equationen
dc.subject.keywordsnonlinear parabolic equationen
dc.subject.keywordssasymptotic behavior of solutionsen
dc.titleParabolic equations with natural growth approximated by nonlocal equationsen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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