Publication
Uniqueness in the Freedericksz transition with weak anchoring
| dc.contributor.author | Costa, Fernando Pestana da | |
| dc.contributor.author | Grinfeld, Michael | |
| dc.contributor.author | Mottram, Nigel J. | |
| dc.contributor.author | Pinto, João Teixeira | |
| dc.date.accessioned | 2010-05-14T12:07:33Z | |
| dc.date.available | 2010-05-14T12:07:33Z | |
| dc.date.issued | 2009-02-11 | |
| dc.description.abstract | 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]. | pt |
| dc.description.version | peerreviewed | |
| dc.identifier.citation | Costa, Fernando Pestana da [et al.] - Uniqueness in the Freedericksz transition with weak anchoring. "Journal of Differential Equations" [Em linha]. ISSN 0022-0396. Nº 246 (2009), p. 2590-2600 | pt |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/1468 | |
| dc.language.iso | eng | pt |
| dc.publisher | Elsevier | pt |
| dc.relation.publisherversion | DOI 10.1016/j.jde.2009.01.033 | pt |
| dc.subject | Freedericksz transition | pt |
| dc.subject | Burgers’ equation | pt |
| dc.subject | Convexity | pt |
| dc.subject | Non-linear boundary value problems | pt |
| dc.subject | Uniqueness of solutions | pt |
| dc.title | Uniqueness in the Freedericksz transition with weak anchoring | pt |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 2600 | pt |
| oaire.citation.startPage | 2590 | pt |
| oaire.citation.title | Journal of Differential Equations | pt |
| person.familyName | Costa | |
| person.familyName | Grinfeld | |
| person.familyName | Teixeira Pinto | |
| person.givenName | Fernando Pestana da | |
| person.givenName | Michael | |
| person.givenName | João | |
| person.identifier.ciencia-id | 1610-6502-E6C5 | |
| person.identifier.orcid | 0000-0002-9072-797X | |
| person.identifier.orcid | 0000-0002-3897-8819 | |
| person.identifier.orcid | 0000-0003-0190-2113 | |
| person.identifier.rid | K-5942-2013 | |
| person.identifier.scopus-author-id | 14827970300 | |
| person.identifier.scopus-author-id | 7402584922 | |
| rcaap.rights | openAccess | pt |
| rcaap.type | article | pt |
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| relation.isAuthorOfPublication.latestForDiscovery | 72748d24-0598-4f36-804e-87eebd0d06af |