A generalized thin-film equation in multidimensional space

✍ Scribed by M. Boutat; S. Hilout; J.-E. Rakotoson; J.-M. Rakotoson

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 405 KB
• Volume: 69
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.06.028

✦ Synopsis

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 blowup 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)].