Abstract

We consider a fourth-order nonlinear parabolic type equation on a twodimensional bounded domain . This equation governs the evolution of the height profile of a thin film in an epitaxial growth process. We show th at such equation endowed with no-flux boundary conditions generates a dissip ative dynamical system under very general assumptions on on a phase-space of L 2 -type. This system possesses a global as well as an exponential attractor. In ad dition, if is smooth enough, we show that every trajectory converges to a single equilibrium by means of a suitable Eojasiewicz‐Simon inequality. An estimate of the convergence rate is also obtained.

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