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MiS Preprint

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

Helmut Abels and Mathias Wilke


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.

Jun 28, 2006
Jun 28, 2006
MSC Codes:
35K55, 35B40, 35Q99, 47H05, 47J35, 80A22
Cahn-Hilliard equation, logarithmic potential, Lojasiewicz-Simon inequality, convergence to steady states, monotone operators

Related publications

2007 Repository Open Access
Helmut Abels and Mathias Wilke

Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy

In: Nonlinear analysis / A, 67 (2007) 11, pp. 3176-3193