Abstract: ABSTRACT: In this paper we study the large time behavior of the solutions to the following nonlinear fourth-order equations ?tu=?e??u,?tu=?u2?2(u3). ?tu=?e??u,?tu=?u2?2(u3). These two PDE were proposed as models of the evolution of crystal surfaces by J. Krug, H.T. Dobbs, and S. Majaniemi (Z. Phys. B, 97,281-291, 1995) and H. Al Hajj Shehadeh, R. V. Kohn, and J. Weare (Phys. D, 240, 1771-1784, 2011), respectively. In particular, we find explicitly computable conditions on the size of the initial data (measured in terms of the norm in a critical space) guaranteeing the global existence and exponential decay to equilibrium in the Wiener algebra and in Sobolev spaces.

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