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The continuity of global attractors for dissipative systems under variation of the domain has been the subject of investigation by many authors. In particular, using techniques developed by D. Henry, the co-authors proved that continuity of attractors (upper and lower) holds for a class of semilinear parabolic problems with nonlinear Neumann boundary conditions under
$C^2$-perturbations of the domain. Our aim here is to extend this result for less regular $C^1$ -perturbations. In order to achieve this goal, it is necessary to find a way to compare the solutions of the problems defined in different regions, which is done by bringing them back to a fixed region. To deal with the nonlinear boundary conditions, it has also been necessary to work in fractional power spaces with negative exponent. |
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