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Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy. (English) Zbl 1121.35018
Summary: 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.

MSC:
35B40 Asymptotic behavior of solutions to PDEs
35K55 Nonlinear parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
47H05 Monotone operators and generalizations
47J35 Nonlinear evolution equations
80A22 Stefan problems, phase changes, etc.
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