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Inertial manifolds for retarded semilinear parabolic equations. (English) Zbl 0954.34064
The aim of the paper is to construct inertial manifolds and to investigate their properties for a class of semilinear parabolic equations with delay. In order to construct inertial manifolds for this case, a spectral gap condition of the same type as for the nonretarded parabolic system is used. The existence of an inertial manifold means that the long-time behaviour of the solutions to the retarded parabolic partial differential equation can be described by a finite-dimensional system of ordinary differential equations without retarded terms.

34K19 Invariant manifolds of functional-differential equations
34G20 Nonlinear differential equations in abstract spaces
35R10 Functional partial differential equations
35K90 Abstract parabolic equations
35B42 Inertial manifolds
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
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