Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection
We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, which may be highly anisotropic. The initial data are assumed to be bounded...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/737220 |
| Acceso en línea: | https://hdl.handle.net/10486/737220 https://dx.doi.org/10.1016/j.matpur.2023.09.009 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlocal diffusion anisotropic stable operators diffusion-convection asymptotic behaviour well-posedness compactness arguments Matemáticas |
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Large-time behaviour for anisotropic stable nonlocal diffusion problems with convectionEndal, JørgenIgnat, Liviu I.Quirós Gracián, FernandoNonlocal diffusionanisotropic stable operatorsdiffusion-convectionasymptotic behaviourwell-posednesscompactness argumentsMatemáticasWe study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, which may be highly anisotropic. The initial data are assumed to be bounded and integrable. The mass of the solution is conserved along the evolution, and the large-time behaviour is given by the source-type solution, with the same mass, of a limit equation that depends on the relative strength of convection and diffusion. When diffusion is stronger than convection the original equation simplifies asymptotically to the purely diffusive nonlocal heat equation. When convection dominates, it does so only in the direction of convection, and the limit equation is still diffusive in the subspace orthogonal to this direction, with a diffusion operator that is a “projection” of the original one onto the subspace. The determination of this projection is one of the main issues of the paper. When convection and diffusion are of the same order the limit equation coincides with the original oneElsevierFacultad de CienciasDepartamento de Matemáticasmatematicas20232023-10-24research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10486/737220https://dx.doi.org/10.1016/j.matpur.2023.09.009reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7372202026-06-23T12:46:27Z |
| dc.title.none.fl_str_mv |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| title |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| spellingShingle |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection Endal, Jørgen Nonlocal diffusion anisotropic stable operators diffusion-convection asymptotic behaviour well-posedness compactness arguments Matemáticas |
| title_short |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| title_full |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| title_fullStr |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| title_full_unstemmed |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| title_sort |
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection |
| dc.creator.none.fl_str_mv |
Endal, Jørgen Ignat, Liviu I. Quirós Gracián, Fernando |
| author |
Endal, Jørgen |
| author_facet |
Endal, Jørgen Ignat, Liviu I. Quirós Gracián, Fernando |
| author_role |
author |
| author2 |
Ignat, Liviu I. Quirós Gracián, Fernando |
| author2_role |
author author |
| dc.contributor.none.fl_str_mv |
Facultad de Ciencias Departamento de Matemáticas matematicas |
| dc.subject.none.fl_str_mv |
Nonlocal diffusion anisotropic stable operators diffusion-convection asymptotic behaviour well-posedness compactness arguments Matemáticas |
| topic |
Nonlocal diffusion anisotropic stable operators diffusion-convection asymptotic behaviour well-posedness compactness arguments Matemáticas |
| description |
We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, which may be highly anisotropic. The initial data are assumed to be bounded and integrable. The mass of the solution is conserved along the evolution, and the large-time behaviour is given by the source-type solution, with the same mass, of a limit equation that depends on the relative strength of convection and diffusion. When diffusion is stronger than convection the original equation simplifies asymptotically to the purely diffusive nonlocal heat equation. When convection dominates, it does so only in the direction of convection, and the limit equation is still diffusive in the subspace orthogonal to this direction, with a diffusion operator that is a “projection” of the original one onto the subspace. The determination of this projection is one of the main issues of the paper. When convection and diffusion are of the same order the limit equation coincides with the original one |
| publishDate |
2023 |
| dc.date.none.fl_str_mv |
2023 2023-10-24 |
| dc.type.none.fl_str_mv |
research article http://purl.org/coar/resource_type/c_2df8fbb1 AM http://purl.org/coar/version/c_ab4af688f83e57aa |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/10486/737220 https://dx.doi.org/10.1016/j.matpur.2023.09.009 |
| url |
https://hdl.handle.net/10486/737220 https://dx.doi.org/10.1016/j.matpur.2023.09.009 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Elsevier |
| publisher.none.fl_str_mv |
Elsevier |
| dc.source.none.fl_str_mv |
reponame:Biblos-e Archivo. Repositorio Institucional de la UAM instname:Universidad Autónoma de Madrid |
| instname_str |
Universidad Autónoma de Madrid |
| reponame_str |
Biblos-e Archivo. Repositorio Institucional de la UAM |
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Biblos-e Archivo. Repositorio Institucional de la UAM |
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1869404414698061824 |
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15,81155 |