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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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