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).
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}, pages = {413--433}, publisher = {Elsevier}, volume = {29}, number = {3}, year = {2012}, doi = {10.1016/j.anihpc.2012.01.003}, zbl = {1308.35123}, mrnumber = {2926242}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.003/} }
TY - JOUR AU - Imbert, C. AU - Mellet, A. TI - Electrified thin films: Global existence of non-negative solutions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2012 SP - 413 EP - 433 VL - 29 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.003/ DO - 10.1016/j.anihpc.2012.01.003 LA - en ID - AIHPC_2012__29_3_413_0 ER -
%0 Journal Article %A Imbert, C. %A Mellet, A. %T Electrified thin films: Global existence of non-negative solutions %J Annales de l'I.H.P. Analyse non linéaire %D 2012 %P 413-433 %V 29 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.01.003/ %R 10.1016/j.anihpc.2012.01.003 %G en %F 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/articles/10.1016/j.anihpc.2012.01.003/
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