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Asymptotic behavior of solution to the Cahn-Hilliard equation. (English) Zbl 0582.34070
The asymptotic behavior of the solution to the initial boundary value problem of the nonlinear Cahn-Hilliard equation and the associated stationary problem have been extensively studied. In particular, it is proved that in the one space dimensional case the associated stationary problem has exactly \(2N+1\) solutions and the solution of the evolution equation converges to a certain equilibrium solution as \(t\to \infty\).

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
Full Text: DOI
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