Thin film arises in various applications from electrochemistry to nano devices, many mathematical tools were adopted to study the problem, e.g. Lie symmetries and conservation laws, however, the variational approach is rare. This paper shows that the semi-inverse method is an effective approach to establishment of a variational formulation for the thin film equation. A detailed derivation process is given, a special skill for construction of a heuristic trial-functional is elucidated.

中文翻译：

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薄膜方程的变分原理

薄膜出现在从电化学到纳米器件的各种应用中，许多数学工具被用来研究这个问题，例如李对称性和守恒定律，然而，变分方法很少见。本文表明，半逆方法是建立薄膜方程变分公式的有效方法。给出了详细的推导过程，阐明了构建启发式试验泛函的特殊技巧。