Electrified thin films: Global existence of non-negative solutions
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, p. 413-433

We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy).

DOI : https://doi.org/10.1016/j.anihpc.2012.01.003
Classification:  35G25,  35K25,  35A01,  35B09
Keywords: Higher order equation, Non-local equation, Thin film equation, Non-negative solutions
@article{AIHPC_2012__29_3_413_0,
     author = {Imbert, C. and Mellet, A.},
     title = {Electrified thin films: Global existence of non-negative solutions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     pages = {413-433},
     doi = {10.1016/j.anihpc.2012.01.003},
     mrnumber = {2926242},
     zbl = {1308.35123},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_3_413_0}
}
Imbert, C.; Mellet, A. Electrified thin films: Global existence of non-negative solutions. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 3, pp. 413-433. doi : 10.1016/j.anihpc.2012.01.003. http://www.numdam.org/item/AIHPC_2012__29_3_413_0/

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