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Convergence to steady states of solutions of the Cahn-Hilliard and Caginalp equations with dynamic boundary conditions. (English) Zbl 1107.35058
Summary: We consider a solution of the Cahn-Hilliard equation or an associated Caginalp problem with dynamic boundary condition in the case of a general potential and prove that under some conditions on the potential it converges, as $$t\to \infty$$, to a stationary solution. The main tool will be the Łojasiewicz-Simon inequality for the underlying energy functional.

##### MSC:
 35K35 Initial-boundary value problems for higher-order parabolic equations 35B35 Stability in context of PDEs 34D05 Asymptotic properties of solutions to ordinary differential equations
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