Abstract
We consider a singular perturbation of the generalized viscous Cahn-Hilliard equation based on constitutive equations introduced by M. E. Gurtin and we establish the existence of a family of inertial manifolds which is continuous with respect to the perturbation parameter $\varepsilon> 0$ as $\varepsilon$ goes to 0. In a recent paper, we proved a similar result for the singular perturbation of the standard viscous Cahn-Hilliard equation, applying a construction due to X. Mora and J. Solà-Morales for equations involving linear self-adjoint operators only. Here we extend the result to the singularly perturbed Cahn-Hilliard-Gurtin equation which contains a non-self-adjoint operator. Our method can be applied to a larger class of nonlinear dynamical systems.
Citation
Ahmed Bonfoh. Maurizio Grasselli. Alain Miranville. "Inertial manifolds for a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation." Topol. Methods Nonlinear Anal. 35 (1) 155 - 185, 2010.
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