Dynamical system for BCF model describing crystal surface growth

This paper treats the initial-boundary value problem for a nonlinear parabolic equation of forth order which was presented by Johnson — Orme — Hunt — Graff — Sudijono — Sauder — Orr [1] in order to describe the interesting phenomena of crystal surface growth under molecular beam epitaxy (MBE). First we construct unique local solutions in a suitable function space by applying the techniques of abstract parabolic evolution equations. Second we establish a priori estimates to obtain the global existence of solutions. Our goal is then to construct a dynamical system determined from the initial-boundary value problem of the model equation.