Some properties of solutions of advection-diffusion equations in R

Detalhes bibliográficos
Autor(a) principal: Guidolin, Patrícia Lisandra
Data de Publicação: 2023
Outros Autores: Schütz, Lineia, Ziebell, Juliana Sartori
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRGS
Texto Completo: http://hdl.handle.net/10183/271769
Resumo: In this paper is provided a proof, using a technique based on energy methods, of the continuity of bounded solutions for the advection-diffusion equations ut + (b(x, t)u k+1)x = µ(t)uxx ∀x ∈ R, t > 0, with initial data u(·, 0) = u0 ∈ L 1 (R) ∩ L∞(R). In respect of the arbitrary advective speed term, it is only assumed that b(x, t) is limited. Also, some known results about existence of solutions of this problem are revised and a discussion of some open problems is presented.
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spelling Guidolin, Patrícia LisandraSchütz, LineiaZiebell, Juliana Sartori2024-02-09T05:06:42Z20230103-9059http://hdl.handle.net/10183/271769001193851In this paper is provided a proof, using a technique based on energy methods, of the continuity of bounded solutions for the advection-diffusion equations ut + (b(x, t)u k+1)x = µ(t)uxx ∀x ∈ R, t > 0, with initial data u(·, 0) = u0 ∈ L 1 (R) ∩ L∞(R). In respect of the arbitrary advective speed term, it is only assumed that b(x, t) is limited. Also, some known results about existence of solutions of this problem are revised and a discussion of some open problems is presented.application/pdfengMatemática contemporânea. Rio de Janeiro. Vol. 56 (2023), p. 20-30Equacões de advecção-difusãoAdvection-diffusion equationsContinuity on Lp normGlobal existenceSome properties of solutions of advection-diffusion equations in Rinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/otherinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001193851.pdf.txt001193851.pdf.txtExtracted Texttext/plain15832http://www.lume.ufrgs.br/bitstream/10183/271769/2/001193851.pdf.txt22b545e413e3d8bcb2e2aefbf5407f41MD52ORIGINAL001193851.pdfTexto completo (inglês)application/pdf523837http://www.lume.ufrgs.br/bitstream/10183/271769/1/001193851.pdfac5655353680ea8a92bc8123e7748f44MD5110183/2717692024-02-10 06:08:05.986539oai:www.lume.ufrgs.br:10183/271769Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2024-02-10T08:08:05Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false
dc.title.pt_BR.fl_str_mv Some properties of solutions of advection-diffusion equations in R
title Some properties of solutions of advection-diffusion equations in R
spellingShingle Some properties of solutions of advection-diffusion equations in R
Guidolin, Patrícia Lisandra
Equacões de advecção-difusão
Advection-diffusion equations
Continuity on Lp norm
Global existence
title_short Some properties of solutions of advection-diffusion equations in R
title_full Some properties of solutions of advection-diffusion equations in R
title_fullStr Some properties of solutions of advection-diffusion equations in R
title_full_unstemmed Some properties of solutions of advection-diffusion equations in R
title_sort Some properties of solutions of advection-diffusion equations in R
author Guidolin, Patrícia Lisandra
author_facet Guidolin, Patrícia Lisandra
Schütz, Lineia
Ziebell, Juliana Sartori
author_role author
author2 Schütz, Lineia
Ziebell, Juliana Sartori
author2_role author
author
dc.contributor.author.fl_str_mv Guidolin, Patrícia Lisandra
Schütz, Lineia
Ziebell, Juliana Sartori
dc.subject.por.fl_str_mv Equacões de advecção-difusão
topic Equacões de advecção-difusão
Advection-diffusion equations
Continuity on Lp norm
Global existence
dc.subject.eng.fl_str_mv Advection-diffusion equations
Continuity on Lp norm
Global existence
description In this paper is provided a proof, using a technique based on energy methods, of the continuity of bounded solutions for the advection-diffusion equations ut + (b(x, t)u k+1)x = µ(t)uxx ∀x ∈ R, t > 0, with initial data u(·, 0) = u0 ∈ L 1 (R) ∩ L∞(R). In respect of the arbitrary advective speed term, it is only assumed that b(x, t) is limited. Also, some known results about existence of solutions of this problem are revised and a discussion of some open problems is presented.
publishDate 2023
dc.date.issued.fl_str_mv 2023
dc.date.accessioned.fl_str_mv 2024-02-09T05:06:42Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10183/271769
dc.identifier.issn.pt_BR.fl_str_mv 0103-9059
dc.identifier.nrb.pt_BR.fl_str_mv 001193851
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url http://hdl.handle.net/10183/271769
dc.language.iso.fl_str_mv eng
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dc.relation.ispartof.pt_BR.fl_str_mv Matemática contemporânea. Rio de Janeiro. Vol. 56 (2023), p. 20-30
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eu_rights_str_mv openAccess
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reponame_str Repositório Institucional da UFRGS
collection Repositório Institucional da UFRGS
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