Convergence to Equilibrium for the Cahn-Hilliard Equation with a Logarithmic Free Energy

Helmut Abels and Mathias Wilke

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Submission date: 28. Jun. 2006
Pages: 27
published in: Nonlinear analysis / A, 67 (2007) 11, p. 3176-3193 
DOI number (of the published article): 10.1016/j.na.2006.10.002
Bibtex
MSC-Numbers: 35K55, 35B40, 35Q99, 47H05, 47J35, 80A22
Keywords and phrases: Cahn-Hilliard equation, logarithmic potential, Lojasiewicz-Simon inequality, convergence to steady states, monotone operators
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Abstract:
In this paper we investigate the asymptotic behavior of the nonlinear Cahn-Hilliard equation with a logarithmic free energy and similar singular free energies. We prove an existence and uniqueness result with the help of monotone operator methods, which differs from the known proofs based on approximation by smooth potentials. Moreover, we apply the Lojasiewicz-Simon inequality to show that each solution converges to a steady state as time tends to infinity.