Convergence of solutions for the fractional Cahn–Hilliard system

Goro Akagi, Giulio Schimperna, Antonio Segatti

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11 Citations (Scopus)


This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of 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 Łojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but C 1 ) nonlinearities.

Original languageEnglish
Pages (from-to)2663-2715
Number of pages53
JournalJournal of Functional Analysis
Issue number9
Publication statusPublished - 2019 May 1


  • Cahn–Hilliard equation
  • Fractional (Dirichlet) Laplacian
  • Long-time behavior of solutions
  • Łojasiewicz–Simon's inequality


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