Invariant manifolds for parabolic equations under perturbation of the domain

Details Invariant manifolds for parabolic equations under perturbation of the domain Invariant manifolds for parabolic equations under perturbation of the domain

2011-09-15

arxiv.org/abs/1109.3260v1

Mathematics

Analysis of PDEs

Scientific paper

We study the effect of domain perturbation on invariant manifolds for semilinear parabolic equations subject to Dirichlet boundary condition. Under Mosco convergence assumption on the domains, we prove the upper and lower semicontinuity of both the local unstable invariant manifold and the local stable invariant manifold near a hyperbolic equilibrium. The continuity results are obtained by keeping track of the construction of invariant manifolds in P. W. Bates and C. K. R. T. Jones [Dynam. Report. Ser. Dynam. Systems Appl. Vol. 2, 1--38, 1989].

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