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A nonlinear diffusion equation governing a surface deformation, which has been derived theoretically for the Marangoni convection, is investigated numerically. By solving an initial value problem under a periodic boundary condition, it is found that the numerical solutions for the surface deformation are classified into three types, i.e., damping, steady and explosive ones depending upon various values of parameters.
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Funada et al. (1986) studied this question.
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