Strong solution for singularly nonautonomous evolution equation with almost sectorial operators

ct. In this paper we consider the singularly nonautonomous evolution problem ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ∈ X, associated with a family of uniformly almost sectorial linear operators A(t) : D ⊂ X → X, that is, a family for which a sector of the complex plane is contained in the...

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Autores: Boldrin Belluzi, Maykel, Caraballo Garrido, Tomás, Dias Nascimento, Marcelo José, Schiabel, Karina
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/142975
Acceso en línea:https://hdl.handle.net/11441/142975
https://doi.org/10.3934/dcds.2022145
Access Level:acceso abierto
Palabra clave:Singularly nonautonomous parabolic problems
almost sectorial operators
regularization
smoothing effect
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spelling Strong solution for singularly nonautonomous evolution equation with almost sectorial operatorsBoldrin Belluzi, MaykelCaraballo Garrido, TomásDias Nascimento, Marcelo JoséSchiabel, KarinaSingularly nonautonomous parabolic problemsalmost sectorial operatorsregularizationsmoothing effectct. In this paper we consider the singularly nonautonomous evolution problem ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ∈ X, associated with a family of uniformly almost sectorial linear operators A(t) : D ⊂ X → X, that is, a family for which a sector of the complex plane is contained in the resolvent of −A(t) and satisfies k(λ + A(t))−1kL(X) ≤ C |λ|α , for some α ∈ (0, 1), uniformly in t. Under a proper condition on the value of α we prove that the linear process associated to the family A(t), t ∈ R, is strongly differentiable and that the singularly nonautonomous problem has a strong solution. An example of a singularly nonautonomous reaction-diffusion equation in a domain with a handle illustrates the abstracts results obtaiAmerican Institute of Mathematical SciencesEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/142975https://doi.org/10.3934/dcds.2022145reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems, 43 (1), 177-208.https://dx.doi.org/10.3934/dcds.2022145info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1429752026-06-17T12:51:07Z
dc.title.none.fl_str_mv Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
title Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
spellingShingle Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
Boldrin Belluzi, Maykel
Singularly nonautonomous parabolic problems
almost sectorial operators
regularization
smoothing effect
title_short Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
title_full Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
title_fullStr Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
title_full_unstemmed Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
title_sort Strong solution for singularly nonautonomous evolution equation with almost sectorial operators
dc.creator.none.fl_str_mv Boldrin Belluzi, Maykel
Caraballo Garrido, Tomás
Dias Nascimento, Marcelo José
Schiabel, Karina
author Boldrin Belluzi, Maykel
author_facet Boldrin Belluzi, Maykel
Caraballo Garrido, Tomás
Dias Nascimento, Marcelo José
Schiabel, Karina
author_role author
author2 Caraballo Garrido, Tomás
Dias Nascimento, Marcelo José
Schiabel, Karina
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Singularly nonautonomous parabolic problems
almost sectorial operators
regularization
smoothing effect
topic Singularly nonautonomous parabolic problems
almost sectorial operators
regularization
smoothing effect
description ct. In this paper we consider the singularly nonautonomous evolution problem ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ∈ X, associated with a family of uniformly almost sectorial linear operators A(t) : D ⊂ X → X, that is, a family for which a sector of the complex plane is contained in the resolvent of −A(t) and satisfies k(λ + A(t))−1kL(X) ≤ C |λ|α , for some α ∈ (0, 1), uniformly in t. Under a proper condition on the value of α we prove that the linear process associated to the family A(t), t ∈ R, is strongly differentiable and that the singularly nonautonomous problem has a strong solution. An example of a singularly nonautonomous reaction-diffusion equation in a domain with a handle illustrates the abstracts results obtai
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/142975
https://doi.org/10.3934/dcds.2022145
url https://hdl.handle.net/11441/142975
https://doi.org/10.3934/dcds.2022145
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems, 43 (1), 177-208.
https://dx.doi.org/10.3934/dcds.2022145
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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