TY - JOUR
AU - Bonfoh, Ahmed
AU - Grasselli, Maurizio
AU - Miranville, Alain
PY - 2010/04/23
Y2 - 2023/03/29
TI - Inertial manifolds for a singular perturbation of the viscous Cahn-Hilliard-Gurtin equation
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 35
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2010.010
SP - 155 - 185
AB - We consider a singularperturbation of the generalized viscous Cahn-Hilliard equationbased on constitutive equations introduced by M. E. Gurtin and we establish the existence of a familyof 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. Sol\`a-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.
ER -