Existence and blow-up of weak solutions for a sixth-order equation related to thin solid films

This paper is concerned with the sixth-order nonlinear uniformly parabolic equation of the form ht=hx(6)+hxxxx+ghxx+(hhxx+phx2+qh2)xx which arises in the description of thin, epitaxially strained films in the presence of wetting intersections with the substrate. Under periodic boundary conditions we prove the existence, uniqueness and regularity of the weak solution. Also, we show the finite-time blow-up under the Dirichlet boundary conditions and obtain the estimates for the blow-up time.