2019/02/22 by Jeremy L. Marzuola, Marzuola, Jeremy L., Sterling Swygert +3 · 1 citation
Computer Science · Engineering · Mathematics · #35Q35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1902.08685
openalex publication_date 2019/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by models for thin films coating cylinders in two physical cases\nproposed by V.I. Kerchman and A.L. Frenkel, we analyze the dynamics of\ncorresponding thin film models. The models are governed by nonlinear,\nfourth-order, degenerate, parabolic PDEs. We prove, given positive and suitably\nregular initial data, the existence of weak solutions in all length scales of\nthe cylinder, where all solutions are only local in time. We also prove that\ngiven a length constraint on the cylinder, long-time and global in time weak\nsolutions exist. This analytical result is motivated by numerical work on\nrelated models in the Ph.D. Thesis of R. Ogrosky in conjunction with multiple\nfurther works jointly worked on by combinations of Camassa, Forest, Lee, the\nfirst author, Ogrosky, Olander, and Vaughn.\n