

Preprint 56/2006
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.