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- W2043188192 abstract "This paper is concerned with the analysis of the nonlinear two-point boundary value problem $varphi '' = lambda xcos ^2 varphi $, $varphi ( -1/2) = 0$, $varphi (1/2) = mpi $. This system models the preferred direction of orientation of liquid crystal molecules flowing in a channel. It is derived by simplification of a formulation in terms of the Ericksen–Leslie equations. The problem has interesting bifurcation and singular-perturbation phenomena. There are infinitely many distinct solution branches, the number growing roughly quadratically with the parameter $lambda $, and individual solutions typically possess $O( 1/sqrt lambda)$ boundary layers at each endpoint and an $O( 1/sqrt[3]{lambda })$ interior layer at $x = 0$. Analytical techniques (involving differential inequalities of Nagumo type) can be used to rigorously prove the existence of the infinite family of stable solutions; while numerical investigations (using the COLSYS/COLNEW and AUTO86 packages) are used to explore the unstable solutions and bifurcation behavior, which involves limit/turning points and simple bifurcation points." @default.
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- W2043188192 date "1994-04-01" @default.
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- W2043188192 title "Analysis of a Simplified Liquid Crystal Shear-Flow Model" @default.
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- W2043188192 doi "https://doi.org/10.1137/s0036139993242972" @default.
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