We investigate the effect of nonlinear feedback control on the oscillatory mode of the long-wave Marangoni instability. Thin liquid film heated from below with a deformable free surface atop a substrate of low thermal conductivity is in our spotlight. We apply nonlinear feedback control to change the excitation of convection from subcritical to supercritical, or to stabilize a definite kind of convective pattern. Nonlinear interaction of traveling waves is examined by means of weakly nonlinear analysis within the amplitude equations. The cases of single wave, of pair of counter-propagating waves, and of three-dimensional two-wave patterns are considered. It is shown that by means of quadratic feedback control it is possible to replace a subcritical bifurcation by a supercritical one, as well as extend the stability region of traveling rolls and traveling rectangles and produce additional structures (traveling squares).

我们研究了非线性反馈控制对长波Marangoni不稳定性振荡模式的影响。从下方加热的液态薄膜具有低导热率的基板顶部具有可变形的自由表面，是我们的关注焦点。我们应用非线性反馈控制将对流的激发从亚临界改变为超临界，或稳定某种对流模式。通过振幅方程中的弱非线性分析来检查行波的非线性相互作用。考虑单波，一对反向传播波和三维两波模式的情况。结果表明，通过二次反馈控制，可以用超临界分叉代替亚临界分叉，