Abstract
We examine spatially periodic solutions of a nonlinear evolution equation describing the Marangoni instability of a planar liquid sheet with both free boundaries. The equation includes energy supply and dissipation terms and exhibits long wave instability. Numerical analysis shows that steady, oscillating and blowup solutions exist for particular parameters of the equations. The reduced amplitude equation explains that the steady and blowup properties of the solutions are determined by the parameter ratios in the original equation.
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