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Uniqueness in the Freedericksz transition with weak anchoring

Da Costa, F.P. and Grinfeld, M. and Mottram, N.J. and Pinto, J.T. and , FCT Portugal (partly supported) (Funder) (2009) Uniqueness in the Freedericksz transition with weak anchoring. Journal of Differential Equations, 246 (7). pp. 2590-2600. ISSN 0022-0396

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    Abstract

    In this paper we consider a boundary value problem for a quasilinear pendulum equation with nonlinear 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 x = −f(x) for ∈ (−T, T), with boundary conditions x = ± T f(x) at = ∓T, for a convex nonlinearity f. By analyzing an associated inviscid Burgers' equation, we prove uniqueness of monotone solutions in the original nonlinear 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,Chapman and Hall, London, 1994 and in I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor and Francis, London, 2003.

    Item type: Article
    ID code: 13697
    Keywords: Freedericksz transition, Burgers' equation, convexity, nonlinear boundar, uniqueness of solutions, value problems, Mathematics, Analysis
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Carolynne Westwood
      Date Deposited: 13 Jan 2010 11:41
      Last modified: 05 Sep 2014 00:18
      URI: http://strathprints.strath.ac.uk/id/eprint/13697

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