Sensitivity equations for measure-valued solutions to transport equations
- Autores
- Ackleh, Azmy S.; Saintier, Nicolas Bernard Claude; Skrzeczkowski, Jakub
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x).
Fil: Ackleh, Azmy S.. State University of Louisiana; Estados Unidos
Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Skrzeczkowski, Jakub. University of Warsaw; Polonia - Materia
-
DIFFERENTIABILITY OF SOLUTIONS
SPACE OF RADON MEASURES
TRANSPORT EQUATIONS
VERY WEAK SOLUTIONS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/150450
Ver los metadatos del registro completo
id |
CONICETDig_4554e1c384246113e01208e1aa9fa889 |
---|---|
oai_identifier_str |
oai:ri.conicet.gov.ar:11336/150450 |
network_acronym_str |
CONICETDig |
repository_id_str |
3498 |
network_name_str |
CONICET Digital (CONICET) |
spelling |
Sensitivity equations for measure-valued solutions to transport equationsAckleh, Azmy S.Saintier, Nicolas Bernard ClaudeSkrzeczkowski, JakubDIFFERENTIABILITY OF SOLUTIONSSPACE OF RADON MEASURESTRANSPORT EQUATIONSVERY WEAK SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x).Fil: Ackleh, Azmy S.. State University of Louisiana; Estados UnidosFil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Skrzeczkowski, Jakub. University of Warsaw; PoloniaAmerican Institute of Mathematical Sciences2020-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/150450Ackleh, Azmy S.; Saintier, Nicolas Bernard Claude; Skrzeczkowski, Jakub; Sensitivity equations for measure-valued solutions to transport equations; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 514-5371547-1063CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/fileOther/PDF/MBE/mbe-17-01-028.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2020028info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:29Zoai:ri.conicet.gov.ar:11336/150450instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:18:29.541CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Sensitivity equations for measure-valued solutions to transport equations |
title |
Sensitivity equations for measure-valued solutions to transport equations |
spellingShingle |
Sensitivity equations for measure-valued solutions to transport equations Ackleh, Azmy S. DIFFERENTIABILITY OF SOLUTIONS SPACE OF RADON MEASURES TRANSPORT EQUATIONS VERY WEAK SOLUTIONS |
title_short |
Sensitivity equations for measure-valued solutions to transport equations |
title_full |
Sensitivity equations for measure-valued solutions to transport equations |
title_fullStr |
Sensitivity equations for measure-valued solutions to transport equations |
title_full_unstemmed |
Sensitivity equations for measure-valued solutions to transport equations |
title_sort |
Sensitivity equations for measure-valued solutions to transport equations |
dc.creator.none.fl_str_mv |
Ackleh, Azmy S. Saintier, Nicolas Bernard Claude Skrzeczkowski, Jakub |
author |
Ackleh, Azmy S. |
author_facet |
Ackleh, Azmy S. Saintier, Nicolas Bernard Claude Skrzeczkowski, Jakub |
author_role |
author |
author2 |
Saintier, Nicolas Bernard Claude Skrzeczkowski, Jakub |
author2_role |
author author |
dc.subject.none.fl_str_mv |
DIFFERENTIABILITY OF SOLUTIONS SPACE OF RADON MEASURES TRANSPORT EQUATIONS VERY WEAK SOLUTIONS |
topic |
DIFFERENTIABILITY OF SOLUTIONS SPACE OF RADON MEASURES TRANSPORT EQUATIONS VERY WEAK SOLUTIONS |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x). Fil: Ackleh, Azmy S.. State University of Louisiana; Estados Unidos Fil: Saintier, Nicolas Bernard Claude. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Skrzeczkowski, Jakub. University of Warsaw; Polonia |
description |
We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, v(x). In particular, we replace the vector field v with a perturbation of the form vh = v0(x) + hv1(x) and let μh t be the solution of θtμh t + θx(vh(x)μh t) = 0: We derive a partial differential equation that is satisfied by the derivative of μh t with respect to h, θh(μh t). We show that this equation has a unique very weak solution on the space Z, being the closure of M(Rd) endowed with the dual norm (C1,α(Rd))*. We also extend the result to the nonlinear case where the vector field depends on μt, i.e., v = v[μt](x). |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-01 |
dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
format |
article |
status_str |
publishedVersion |
dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/150450 Ackleh, Azmy S.; Saintier, Nicolas Bernard Claude; Skrzeczkowski, Jakub; Sensitivity equations for measure-valued solutions to transport equations; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 514-537 1547-1063 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/150450 |
identifier_str_mv |
Ackleh, Azmy S.; Saintier, Nicolas Bernard Claude; Skrzeczkowski, Jakub; Sensitivity equations for measure-valued solutions to transport equations; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 17; 1; 1-2020; 514-537 1547-1063 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.aimspress.com/fileOther/PDF/MBE/mbe-17-01-028.pdf info:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2020028 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
American Institute of Mathematical Sciences |
publisher.none.fl_str_mv |
American Institute of Mathematical Sciences |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
_version_ |
1844614147752329216 |
score |
13.070432 |