A generalized thin-film equation in multidimensional space

This paper deals with the existence and nonnegativity of the weak periodic-domain solution for a degenerate fourth-order parabolic equation modeling the evolution of thin films. This study in the multidimensional domain follows the recent results related to the resolution in one-dimensional space [J.E. Rakotoson, J.M. Rakotoson, C. Verbeke, Generalized lubrification models blow-up and global existence, RACSAM 99 (2) (2005) 235–241; C. Verbeke, Quelques modèles d’équations d’évolution de surfaces: Explosion en temps fini et diverses propriétés qualitatives, Thèse de doctorat de l’Université de Poitiers (15 Décembre 2005); J.E. Rakotoson, J.M. Rakotoson, C. Verbeke, Higher-order equations related to thin film: Blow up and global existence, the influence of the initial data, (submitted for publication)].