On the thin-film equation with nonlinear surface tension term

TL;DR

This thesis studies a one-dimensional thin-film equation with nonlinear surface tension, establishing the existence of weak solutions and their nonnegativity through energy and entropy estimates.

Contribution

It introduces new analytical techniques to prove existence and nonnegativity for solutions of the nonlinear thin-film equation.

Findings

Existence of weak solutions established.

Nonnegativity of solutions proven.

Energy and entropy methods applied successfully.

Abstract

In this thesis, we consider the thin-film equation with nonlinear surface tension term in one space dimension. Relying on the corresponding energy and entropy estimates, we prove existence of weak solutions as well as nonnegativity results.