Numerical solution of the cauchy problem for thin film equation

The thin-film equation arising in numerous physical applications describes the surface-tension-driven evolution of thin viscous liquid films on a solid surface. The application areas include flow behavior of paints and other surface coatings, chemical, and nuclear reactor design, agrochemical applications, as well as several biofluid applications including thin films on the cornea and in the lungs. Mathematically, it is a fourth-order degenerate diffusion equation. The analysis of such equations is doubly complex due to the nonlinearity and the high order. After the required background and the necessary information are given in the first chapter of the thesis, the extinction behavior of a fourth order degenerate diffusion equation in a bounded domain that models the flow of a viscous fluid over the edges at which zero contact angle conditions has been studied.