Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions

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On the Caginalp system with dynamic boundary conditions and singular potentials (2009, methodology): “Indeed, we saw in Theorem 3.2 that the solutions are regular andstrictlyseparatedfromthesingularities ±1. Consequently,thenonlinearity ˜ f(u) is bounded in L ∞ (). Thus the arguments of [ 9 ] are still valid in our case (see in”
Long time behavior of the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions (2010, methodology): “As a final step, we apply the so-called Simon-�Lojasiewicz method (see, e.g., [ 6 ]) to prove that, under additional assumptions on the nonlinear terms, the ω-limit set of any trajectory consists of a single point.”
A Cahn–Hilliard model in bounded domains with permeable walls (2006, methodology): “We note that (1.12)–(1.13) still form elliptic boundary value problems in the sense of Agmon & Douglis & Nirenberg [3], Hörmander [14], Peetre [22] or Vǐsik [26].”
Lyapunov functions and convergence to steady state for differential equations of fractional order (2008, unknown): “[3], [ 5 ], [10], [13], [15], [20], and the references given therein.”