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parabolic integrodifferential equations; invariant manifolds; functional equations; analytic semigroup; Banach space; resolvent operator; interpolation spaces; center manifold; parabolic functional equation; infinite delay; solution semigroup
The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
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