On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary

Detalhes bibliográficos
Autor(a) principal: de Almeida, Marcelo F.
Data de Publicação: 2017
Outros Autores: Ferreira, Lucas C. F., Precioso, Juliana C. [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1007/s11118-016-9595-5
http://hdl.handle.net/11449/173527
Resumo: This paper concerns with the heat equation in the half-space ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a well-posedness result that allows us to consider critical potentials with infinite many singularities and anisotropy. Motivated by potential profiles of interest, the analysis is performed in weak Lp-spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in ℝ+n. Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis Oxn⃗.
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spelling On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the BoundaryHeat equationLorentz spacesNonlinear boundary conditionsSelf-similaritySingular potentialsSymmetryThis paper concerns with the heat equation in the half-space ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a well-posedness result that allows us to consider critical potentials with infinite many singularities and anisotropy. Motivated by potential profiles of interest, the analysis is performed in weak Lp-spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in ℝ+n. Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis Oxn⃗.Departamento de Matemática Universidade Federal de SergipeDepartamento de Matemática Universidade Estadual de CampinasDepartamento de Matemática Unesp-IBILCEDepartamento de Matemática Unesp-IBILCEUniversidade Federal de Sergipe (UFS)Universidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)de Almeida, Marcelo F.Ferreira, Lucas C. F.Precioso, Juliana C. [UNESP]2018-12-11T17:06:06Z2018-12-11T17:06:06Z2017-03-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article589-608application/pdfhttp://dx.doi.org/10.1007/s11118-016-9595-5Potential Analysis, v. 46, n. 3, p. 589-608, 2017.1572-929X0926-2601http://hdl.handle.net/11449/17352710.1007/s11118-016-9595-52-s2.0-849887365082-s2.0-84988736508.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengPotential Analysis1,510info:eu-repo/semantics/openAccess2023-12-07T06:18:15Zoai:repositorio.unesp.br:11449/173527Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:42:50.841716Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
title On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
spellingShingle On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
de Almeida, Marcelo F.
Heat equation
Lorentz spaces
Nonlinear boundary conditions
Self-similarity
Singular potentials
Symmetry
title_short On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
title_full On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
title_fullStr On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
title_full_unstemmed On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
title_sort On the Heat Equation with Nonlinearity and Singular Anisotropic Potential on the Boundary
author de Almeida, Marcelo F.
author_facet de Almeida, Marcelo F.
Ferreira, Lucas C. F.
Precioso, Juliana C. [UNESP]
author_role author
author2 Ferreira, Lucas C. F.
Precioso, Juliana C. [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Federal de Sergipe (UFS)
Universidade Estadual de Campinas (UNICAMP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv de Almeida, Marcelo F.
Ferreira, Lucas C. F.
Precioso, Juliana C. [UNESP]
dc.subject.por.fl_str_mv Heat equation
Lorentz spaces
Nonlinear boundary conditions
Self-similarity
Singular potentials
Symmetry
topic Heat equation
Lorentz spaces
Nonlinear boundary conditions
Self-similarity
Singular potentials
Symmetry
description This paper concerns with the heat equation in the half-space ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a well-posedness result that allows us to consider critical potentials with infinite many singularities and anisotropy. Motivated by potential profiles of interest, the analysis is performed in weak Lp-spaces in which we prove linear estimates for some boundary operators arising from the Duhamel integral formulation in ℝ+n. Moreover, we investigate qualitative properties of solutions like self-similarity, positivity and symmetry around the axis Oxn⃗.
publishDate 2017
dc.date.none.fl_str_mv 2017-03-01
2018-12-11T17:06:06Z
2018-12-11T17:06:06Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s11118-016-9595-5
Potential Analysis, v. 46, n. 3, p. 589-608, 2017.
1572-929X
0926-2601
http://hdl.handle.net/11449/173527
10.1007/s11118-016-9595-5
2-s2.0-84988736508
2-s2.0-84988736508.pdf
url http://dx.doi.org/10.1007/s11118-016-9595-5
http://hdl.handle.net/11449/173527
identifier_str_mv Potential Analysis, v. 46, n. 3, p. 589-608, 2017.
1572-929X
0926-2601
10.1007/s11118-016-9595-5
2-s2.0-84988736508
2-s2.0-84988736508.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Potential Analysis
1,510
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 589-608
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808129108707639296

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