Publicação
Uniqueness in the Freedericksz transition with weak anchoring
| Resumo: | In this paper we consider a boundary value problem for a quasilinear pendulum equation with non-linear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the problem into the equation xττ = −f (x) for τ ∈ (−T , T ), with boundary conditions xτ = ±βT f (x) at τ = ∓T , for a convex non-linearity f . By analysing an associated inviscid Burgers’ equation, we prove uniqueness of monotone solutions in the original non-linear boundary value problem. This result has been for many years conjectured in the liquid crystals literature, e.g. in [E.G. Virga, Variational Theories for Liquid Crystals, Appl. Math. Math. Comput., vol. 8, Chapman & Hall, London, 1994] and in [I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor & Francis, London, 2003]. |
|---|---|
| Autores principais: | Costa, Fernando Pestana da |
| Outros Autores: | Grinfeld, Michael; Mottram, Nigel J.; Pinto, João Teixeira |
| Assunto: | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| Ano: | 2009 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Aberta |
| Idioma: | inglês |
| Origem: | Repositório Aberto da Universidade Aberta |
| _version_ | 1877781777484873728 |
|---|---|
| author | Costa, Fernando Pestana da |
| author2 | Grinfeld, Michael Mottram, Nigel J. Pinto, João Teixeira |
| author2_role | author author author |
| author_facet | Costa, Fernando Pestana da Grinfeld, Michael Mottram, Nigel J. Pinto, João Teixeira |
| author_role | author |
| contributor_name_str_mv | Repositório Aberto |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Costa, Fernando Pestana da\",\"Person.identifier.cienciaID\":\"1610-6502-E6C5\",\"Person.identifier.orcid\":\"0000-0002-9072-797X\",\"Person.identifier.researcherID\":\"K-5942-2013\",\"Person.identifier.scopusAuthorID\":\"14827970300\"},{\"Person.name\":\"Grinfeld, Michael\",\"Person.identifier.orcid\":\"0000-0002-3897-8819\"},{\"Person.name\":\"Mottram, Nigel J.\"},{\"Person.name\":\"Pinto, João Teixeira\",\"Person.identifier.orcid\":\"0000-0003-0190-2113\",\"Person.identifier.scopusAuthorID\":\"7402584922\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | Repositório Aberto |
| datacite.creators.creator.creatorName.fl_str_mv | Costa, Fernando Pestana da Grinfeld, Michael Mottram, Nigel J. Pinto, João Teixeira |
| datacite.date.Accepted.fl_str_mv | 2009-02-11T00:00:00Z |
| datacite.date.available.fl_str_mv | 2010-05-14T12:07:33Z |
| datacite.date.embargoed.fl_str_mv | 2010-05-14T12:07:33Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| datacite.titles.title.fl_str_mv | Uniqueness in the Freedericksz transition with weak anchoring |
| dc.contributor.none.fl_str_mv | Repositório Aberto |
| dc.creator.none.fl_str_mv | Costa, Fernando Pestana da Grinfeld, Michael Mottram, Nigel J. Pinto, João Teixeira |
| dc.date.Accepted.fl_str_mv | 2009-02-11T00:00:00Z |
| dc.date.available.fl_str_mv | 2010-05-14T12:07:33Z |
| dc.date.embargoed.fl_str_mv | 2010-05-14T12:07:33Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10400.2/1468 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| dc.title.fl_str_mv | Uniqueness in the Freedericksz transition with weak anchoring |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | In this paper we consider a boundary value problem for a quasilinear pendulum equation with non-linear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the problem into the equation xττ = −f (x) for τ ∈ (−T , T ), with boundary conditions xτ = ±βT f (x) at τ = ∓T , for a convex non-linearity f . By analysing an associated inviscid Burgers’ equation, we prove uniqueness of monotone solutions in the original non-linear boundary value problem. This result has been for many years conjectured in the liquid crystals literature, e.g. in [E.G. Virga, Variational Theories for Liquid Crystals, Appl. Math. Math. Comput., vol. 8, Chapman & Hall, London, 1994] and in [I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor & Francis, London, 2003]. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://repositorioaberto.uab.pt/bitstreams/b9096fc0-238e-4641-8ea0-a40bb0c81583/download |
| id | raberto_fa2125f85e41fe38340c556f2bb1d620 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10400.2/1468 |
| inst_facet_str | urn:organizationAcronym:raberto{{{_:::_}}}Universidade Aberta |
| instacron_str | raberto |
| institution | Universidade Aberta |
| instname_str | Universidade Aberta |
| language | eng |
| network_acronym_str | raberto |
| network_name_str | Repositório Aberto da Universidade Aberta |
| oai_identifier_str | oai:repositorioaberto.uab.pt:10400.2/1468 |
| organization_str_mv | urn:organizationAcronym:raberto |
| person_str_mv | Costa, Fernando Pestana da Costa, Fernando Pestana da https://www.ciencia-id.pt/1610-6502-E6C5 1610-6502-E6C5 http://orcid.org/0000-0002-9072-797X 0000-0002-9072-797X Grinfeld, Michael Grinfeld, Michael http://orcid.org/0000-0002-3897-8819 0000-0002-3897-8819 Mottram, Nigel J. Pinto, João Teixeira Pinto, João Teixeira http://orcid.org/0000-0003-0190-2113 0000-0003-0190-2113 |
| publishDate | 2009 |
| publisher.none.fl_str_mv | Elsevier |
| repo_facet_str | urn:repositoryAcronym:raberto{{{_:::_}}}Repositório Aberto da Universidade Aberta |
| reponame_str | Repositório Aberto da Universidade Aberta |
| repository_id_str | urn:repositoryAcronym:raberto |
| service_str_mv | urn:repositoryAcronym:raberto |
| spelling | engElsevierptIn this paper we consider a boundary value problem for a quasilinear pendulum equation with non-linear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the problem into the equation xττ = −f (x) for τ ∈ (−T , T ), with boundary conditions xτ = ±βT f (x) at τ = ∓T , for a convex non-linearity f . By analysing an associated inviscid Burgers’ equation, we prove uniqueness of monotone solutions in the original non-linear boundary value problem. This result has been for many years conjectured in the liquid crystals literature, e.g. in [E.G. Virga, Variational Theories for Liquid Crystals, Appl. Math. Math. Comput., vol. 8, Chapman & Hall, London, 1994] and in [I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor & Francis, London, 2003].application/pdfptUniqueness in the Freedericksz transition with weak anchoringPersonalCosta, Fernando Pestana daDSpacehttp://dspace.org/items/72748d24-0598-4f36-804e-87eebd0d06afDSpacehttp://dspace.org/items/72748d24-0598-4f36-804e-87eebd0d06afCostaFernando Pestana daCiência IDhttps://www.ciencia-id.pt1610-6502-E6C5ORCIDhttp://orcid.org0000-0002-9072-797XResearcher IDhttps://www.researcherid.comK-5942-2013Scopus Author IDhttps://www.scopus.com14827970300PersonalGrinfeld, MichaelDSpacehttp://dspace.org/items/6057da1f-64bf-439d-8b2c-0f2282e1ef91DSpacehttp://dspace.org/items/6057da1f-64bf-439d-8b2c-0f2282e1ef91GrinfeldMichaelORCIDhttp://orcid.org0000-0002-3897-8819Mottram, Nigel J.PersonalPinto, João TeixeiraDSpacehttp://dspace.org/items/378f92b2-9a55-4997-b135-4e099cd76d84DSpacehttp://dspace.org/items/378f92b2-9a55-4997-b135-4e099cd76d84PintoJoão TeixeiraORCIDhttp://orcid.org0000-0003-0190-2113Scopus Author IDhttps://www.scopus.com7402584922HostingInstitutionOrganizationalRepositório Abertoe-mailmailto:repositorio_aberto@uab.ptrepositorio_aberto@uab.ptISSNIsPartOf0022-03962010-05-14T12:07:33Z2009-02-112009-02-11T00:00:00ZHandlehttp://hdl.handle.net/10400.2/1468http://purl.org/coar/access_right/c_abf2open accessFreedericksz transitionBurgers’ equationConvexityNon-linear boundary value problemsUniqueness of solutions238109 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorioaberto.uab.pt/bitstreams/b9096fc0-238e-4641-8ea0-a40bb0c81583/downloadJournal of Differential Equations25902600 |
| spellingShingle | Uniqueness in the Freedericksz transition with weak anchoring Costa, Fernando Pestana da Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| status | SINGLETON |
| subject.fl_str_mv | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| title | Uniqueness in the Freedericksz transition with weak anchoring |
| title_full | Uniqueness in the Freedericksz transition with weak anchoring |
| title_fullStr | Uniqueness in the Freedericksz transition with weak anchoring |
| title_full_unstemmed | Uniqueness in the Freedericksz transition with weak anchoring |
| title_short | Uniqueness in the Freedericksz transition with weak anchoring |
| title_sort | Uniqueness in the Freedericksz transition with weak anchoring |
| topic | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| topic_facet | Freedericksz transition Burgers’ equation Convexity Non-linear boundary value problems Uniqueness of solutions |
| url | http://hdl.handle.net/10400.2/1468 |
| visible | 1 |
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