| Abstract: |
| This talk is concerned with the Cauchy-Dirichlet problem for fractional Cahn-Hilliard equations. We shall discuss global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called \L ojasiewicz-Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities. This talk is based on a joint work with G. Schimperna and A. Segatti (Pavia, IT). |
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