Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/1468
Título: Uniqueness in the Freedericksz transition with weak anchoring
Autor: Costa, Fernando Pestana da
Grinfeld, Michael
Mottram, Nigel J.
Pinto, João Teixeira
Palavras-chave: Freedericksz transition
Burgers’ equation
Convexity
Non-linear boundary value problems
Uniqueness of solutions
Data: 11-Fev-2009
Editora: Elsevier
Citação: COSTA, Fernando Pestana da [et al.] - Uniqueness in the Freedericksz transition with weak anchoring. "Journal of Differential Equations". ISSN 0022-0396. 246 (2009), p. 2590–2600
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].
URI: http://hdl.handle.net/10400.2/1468
ISSN: 0022-0396
Versão do Editor: DOI 10.1016/j.jde.2009.01.033
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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