no. 3
Electrified thin films: Global existence of non-negative solutions
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 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 : 10.1016/j.anihpc.2012.01.003
Classification : 35G25, 35K25, 35A01, 35B09
Mots clés : Higher order equation, Non-local equation, Thin film equation, Non-negative solutions 
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     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},
     pages = {413--433},
     publisher = {Elsevier},
     volume = {29},
     number = {3},
     year = {2012},
     doi = {10.1016/j.anihpc.2012.01.003},
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     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.003/}
}
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Imbert, C.; Mellet, A. Electrified thin films: Global existence of non-negative solutions. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 3, pp. 413-433. doi : 10.1016/j.anihpc.2012.01.003. http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.003/

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