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Domain perturbation and invariant manifolds. (English) Zbl 1257.35024
Summary: We consider a reaction-diffusion equation defined on a sequence of bounded open sets \({(\Omega_n)_n \in \mathbb{N}}\), converging to \({\Omega}\) in the sense of Mosco, and we prove stability of invariant manifolds of the flux with respect to domain perturbation.

MSC:
35B20 Perturbations in context of PDEs
35K58 Semilinear parabolic equations
35B35 Stability in context of PDEs
35B42 Inertial manifolds
35K20 Initial-boundary value problems for second-order parabolic equations
35K57 Reaction-diffusion equations
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