Stability analysis in the weak nonlinear domain and for infinite aspect ratios allows us to determine a region of physical parameters in which hexagonal and cylindrical convective cells can coexist in the Bénard-Marangoni instability. The stability of the two different types of patterns is also examined for finite boxes with rigid lateral boundaries by use of a partial differential equation of a generalized Ginzburg-Landau type for the temperature field. Numerical solutions of this equation are presented.
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Bestehorn et al. (1987) studied this question.
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