Convergence to equilibrium for the Cahn–Hilliard equation with a logarithmic free energy |
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Authors: | Helmut Abels Mathias Wilke |
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Institution: | 1. Max Planck Institute for Mathematics in Science, Inselstr. 22, 04103 Leipzig, Germany;2. Fachbereich Mathematik und Informatik, Institut für Analysis, Martin-Luther-Universität Halle-Wittenberg, 06099 Halle, Saale, Germany |
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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. |
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Keywords: | 35K55 35B40 35Q99 47H05 47J35 80A22 |
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