Journal of Mathematical Chemistry

, Volume 57, Issue 9, pp 2075–2081 | Cite as

A variational principle for a thin film equation

  • Ji-Huan HeEmail author
  • Chang Sun
Original Paper


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.


Variational theory Special function Trial-functional Nanoscale adhesion Coating Wetting 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ScienceXi’an University of Architecture and TechnologyXi’anChina
  2. 2.Qujing Normal UniversityQujingChina

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