| Contents |
| In this article, we are interested in the
study of the asymptotic behavior, in terms
of finite-dimensional attractors,
of a generalization of the Cahn-Hilliard
equation with a fidelity term (integrated over
$\Omega\backslash D$ instead of the entire domain
$\Omega$, $D \subset \subset \Omega$). Such a model has, in particular, applications
in image inpainting. The difficulty here is that we
no longer have the conservation of mass, i.e. of the spatial average
of the order parameter $u$, as in the Cahn-Hilliard equation. Instead, we prove
that the spatial average of $u$ is dissipative.
We finally give some numerical simulations which confirm previous ones on the
efficiency of the model. |
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