| Abstract: |
| We consider the initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular potential. We show that any weak solution converges to a single equilibrium using only minimal assumptions, i.e., the existence of a global weak solution satisfying an energy inequality. This result also holds in the three-dimensional case, which was an open problem so far due to the lack of regularity of solutions, especially when the mobility is just a continuous function. This novel method is robust and can be used also for other models like, for instance, Cahn--Hilliard-Navier--Stokes type systems with unmatched densities and viscosities as the one proposed by Abels, Garcke, and Gr\{u}n (Math. Models Methods Appl. Sci. 22, 2012). |
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