Quasivariational solutions for first order quasilinear equations with gradient constraint
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/19984 |
Resumo: | We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable <em> a priori</em> estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results. |
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Quasivariational solutions for first order quasilinear equations with gradient constraintScience & TechnologyWe prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable <em> a priori</em> estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results.Fundação para a Ciência e TecnologiaSpringerUniversidade do MinhoSantos, LisaRodrigues, José Francisco20122012-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/19984eng0003-952710.1007/s00205-012-0511-xhttp://dx.doi.org/10.1007/s00205-012-0511-xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:17:12Zoai:repositorium.sdum.uminho.pt:1822/19984Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:09:46.877828Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
title |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
spellingShingle |
Quasivariational solutions for first order quasilinear equations with gradient constraint Santos, Lisa Science & Technology |
title_short |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
title_full |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
title_fullStr |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
title_full_unstemmed |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
title_sort |
Quasivariational solutions for first order quasilinear equations with gradient constraint |
author |
Santos, Lisa |
author_facet |
Santos, Lisa Rodrigues, José Francisco |
author_role |
author |
author2 |
Rodrigues, José Francisco |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Santos, Lisa Rodrigues, José Francisco |
dc.subject.por.fl_str_mv |
Science & Technology |
topic |
Science & Technology |
description |
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable <em> a priori</em> estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012 2012-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/19984 |
url |
http://hdl.handle.net/1822/19984 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0003-9527 10.1007/s00205-012-0511-x http://dx.doi.org/10.1007/s00205-012-0511-x |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799132524687917056 |