On Qualitative Behaviour of Solutions to a Thin Film Equation with a Source Term

Abstract

In this article, we study a one-dimensional degenerate fourth-order parabolic equation (a thin-film model) with a source term. We prove existence of generalized weak solutions for the case $$n>0$$ and study interface propagation properties like: finite speed propagation and waiting time phenomenon for the case $$1<n<2$$ . Our analysis is based on applications of global and local energy-entropy a priori estimates. Also, we illustrate some of our main analytical results by numerical simulations.