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A variational principle for a thin film equation

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Abstract

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.

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Authors and Affiliations

  1. School of Science, Xi’an University of Architecture and Technology, Xi’an, 710055, China

    Ji-Huan He

  2. Qujing Normal University, Sanjiang Avenue, Economic Development Zone, Qujing, Yunnan, China

    Chang Sun

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  1. Ji-Huan He
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  2. Chang Sun
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He, JH., Sun, C. A variational principle for a thin film equation. J Math Chem 57, 2075–2081 (2019). https://doi.org/10.1007/s10910-019-01063-8

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  • DOI: https://doi.org/10.1007/s10910-019-01063-8

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