The evolution equation and the eigenvalue problem for the Laplacian in a regular tree
Resumen:
In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem, which provides the fundamental tool for describing the long-time dynamics. First, we prove existence and uniqueness of solutions when the initial condition is compatible with the boundary condition. Next, we address the asymptotic behavior of the solutions and show that they decay to zero exponentially fast. This decay rate is determined by the associated first eigenvalue, which we also analyze in detail
| 2026 | |
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Agencia Nacional de Investigación e Innovación Fondo Vaz Ferreira |
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Laplacian operator Regular tree Asymptotic behavior Ciencias Naturales y Exactas Matemáticas |
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| Inglés | |
| Agencia Nacional de Investigación e Innovación | |
| REDI | |
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https://hdl.handle.net/20.500.12381/5576
https://doi.org/10.48550/arXiv.2506.13728 |
|
| Acceso abierto | |
| Reconocimiento-SinObraDerivada 4.0 Internacional. (CC BY-ND) |
| _version_ | 1873394386013782016 |
|---|---|
| author | Del Pezzo, Leandro M. |
| author2 | Frevenza, Nicolas Rossi, Julio |
| author2_role | author author |
| author_facet | Del Pezzo, Leandro M. Frevenza, Nicolas Rossi, Julio |
| author_role | author |
| bitstream.checksum.fl_str_mv | a4ce09f01b5dd771727aa05c73851623 e21f6dd729ea451369b6ca2b52752863 |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 |
| bitstream.url.fl_str_mv | https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5576/2/license.txt https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5576/1/primer_autovalor_v8.pdf |
| collection | REDI |
| dc.creator.none.fl_str_mv | Del Pezzo, Leandro M. Frevenza, Nicolas Rossi, Julio |
| dc.date.accessioned.none.fl_str_mv | 2026-06-09T15:28:28Z |
| dc.date.available.none.fl_str_mv | 2026-06-09T15:28:28Z |
| dc.date.issued.none.fl_str_mv | 2026 |
| dc.description.abstract.none.fl_txt_mv | In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem, which provides the fundamental tool for describing the long-time dynamics. First, we prove existence and uniqueness of solutions when the initial condition is compatible with the boundary condition. Next, we address the asymptotic behavior of the solutions and show that they decay to zero exponentially fast. This decay rate is determined by the associated first eigenvalue, which we also analyze in detail |
| dc.description.sponsorship.none.fl_txt_mv | Agencia Nacional de Investigación e Innovación Fondo Vaz Ferreira |
| dc.identifier.anii.es.fl_str_mv | FCE_3_2024_1_181302 |
| dc.identifier.doi.none.fl_str_mv | https://doi.org/10.48550/arXiv.2506.13728 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12381/5576 |
| dc.language.iso.none.fl_str_mv | eng |
| dc.relation.none.fl_str_mv | https://hdl.handle.net/20.500.12381/5567 https://hdl.handle.net/20.500.12381/5568 https://hdl.handle.net/20.500.12381/5575 |
| dc.rights.*.fl_str_mv | Acceso abierto |
| dc.rights.license.none.fl_str_mv | Reconocimiento-SinObraDerivada 4.0 Internacional. (CC BY-ND) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:REDI instname:Agencia Nacional de Investigación e Innovación instacron:Agencia Nacional de Investigación e Innovación |
| dc.subject.anii.none.fl_str_mv | Ciencias Naturales y Exactas Matemáticas |
| dc.subject.es.fl_str_mv | Laplacian operator Regular tree Asymptotic behavior |
| dc.title.none.fl_str_mv | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| description | In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem, which provides the fundamental tool for describing the long-time dynamics. First, we prove existence and uniqueness of solutions when the initial condition is compatible with the boundary condition. Next, we address the asymptotic behavior of the solutions and show that they decay to zero exponentially fast. This decay rate is determined by the associated first eigenvalue, which we also analyze in detail |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | REDI_2afc1e4cafa9e039b4d142f863ff9b2c |
| identifier_str_mv | FCE_3_2024_1_181302 |
| instacron_str | Agencia Nacional de Investigación e Innovación |
| institution | Agencia Nacional de Investigación e Innovación |
| instname_str | Agencia Nacional de Investigación e Innovación |
| language | eng |
| network_acronym_str | REDI |
| network_name_str | REDI |
| oai_identifier_str | oai:redi.anii.org.uy:20.500.12381/5576 |
| publishDate | 2026 |
| reponame_str | REDI |
| repository.mail.fl_str_mv | jmaldini@anii.org.uy |
| repository.name.fl_str_mv | REDI - Agencia Nacional de Investigación e Innovación |
| repository_id_str | 9421 |
| rights_invalid_str_mv | Reconocimiento-SinObraDerivada 4.0 Internacional. (CC BY-ND) Acceso abierto |
| spelling | Reconocimiento-SinObraDerivada 4.0 Internacional. (CC BY-ND)Acceso abiertoinfo:eu-repo/semantics/openAccess2026-06-09T15:28:28Z2026-06-09T15:28:28Z2026https://hdl.handle.net/20.500.12381/5576FCE_3_2024_1_181302https://doi.org/10.48550/arXiv.2506.13728In this paper, our main goal is to study the evolution problem associated with the Laplacian operator with Dirichlet boundary conditions on a regular tree. To this end, we place special emphasis on the associated first eigenvalue problem, which provides the fundamental tool for describing the long-time dynamics. First, we prove existence and uniqueness of solutions when the initial condition is compatible with the boundary condition. Next, we address the asymptotic behavior of the solutions and show that they decay to zero exponentially fast. This decay rate is determined by the associated first eigenvalue, which we also analyze in detailAgencia Nacional de Investigación e InnovaciónFondo Vaz Ferreiraenghttps://hdl.handle.net/20.500.12381/5567https://hdl.handle.net/20.500.12381/5568https://hdl.handle.net/20.500.12381/5575Laplacian operatorRegular treeAsymptotic behaviorCiencias Naturales y ExactasMatemáticasThe evolution equation and the eigenvalue problem for the Laplacian in a regular treePreprintinfo:eu-repo/semantics/preprintUniversidad de la República. Facultad de Ciencias Económicas y de Administración//Ciencias Naturales y Exactas/Matemáticas/Matemáticasreponame:REDIinstname:Agencia Nacional de Investigación e Innovacióninstacron:Agencia Nacional de Investigación e InnovaciónDel Pezzo, Leandro M.Frevenza, NicolasRossi, JulioLICENSElicense.txtlicense.txttext/plain; charset=utf-84967https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5576/2/license.txta4ce09f01b5dd771727aa05c73851623MD52ORIGINALprimer_autovalor_v8.pdfprimer_autovalor_v8.pdfapplication/pdf361191https://redi.anii.org.uy/jspui/bitstream/20.500.12381/5576/1/primer_autovalor_v8.pdfe21f6dd729ea451369b6ca2b52752863MD5120.500.12381/55762026-06-09 13:45:47.955oai:redi.anii.org.uy:20.500.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Institucionalhttps://redi.anii.org.uy/Organismo de gobiernohttps://www.anii.org.uy/https://redi.anii.org.uy/oai/requestjmaldini@anii.org.uyUruguayopendoar:94212026-06-09T16:45:47REDI - Agencia Nacional de Investigación e Innovaciónfalse |
| spellingShingle | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree Del Pezzo, Leandro M. Laplacian operator Regular tree Asymptotic behavior Ciencias Naturales y Exactas Matemáticas |
| title | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| title_full | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| title_fullStr | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| title_full_unstemmed | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| title_short | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| title_sort | The evolution equation and the eigenvalue problem for the Laplacian in a regular tree |
| topic | Laplacian operator Regular tree Asymptotic behavior Ciencias Naturales y Exactas Matemáticas |
| url | https://hdl.handle.net/20.500.12381/5576 https://doi.org/10.48550/arXiv.2506.13728 |
