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MiS Preprint
56/2006

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

Helmut Abels and Mathias Wilke

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.

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

Related publications

inJournal
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