The Mathematical Theory of Thin Film Evolution

Thin films;Lubrication approximation;Lyapunov functional;Energy dissipation;Weak solution;Equipartition

Ulusoy, Suleyman ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Thin films;    Lubrication approximation;    Lyapunov functional;    Energy dissipation;    Weak solution;    Equipartition;   

Others  :  https://smartech.gatech.edu/bitstream/1853/16213/1/ulusoy_suleyman_200708_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We try toexplain the mathematical theory of thin liquid film evolution. We start with introducing physical processes in which thin film evolution plays an important role. Derivation of the classical thin filmequation and existing mathematical theory in the literature are also introduced. To explain the thin film evolution we derive a new family of degenerate parabolic equations. We prove results on existence, uniqueness, long time behavior, regularity and support properties of solutions for this equation. At the end of the thesis we consider the classical thin film Cauchy problem on the whole real line for which we use asymptotic equipartition to show H^1(R) convergence of solutions to the unique self-similar solution.