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Inertial manifolds for a class of non-autonomous semilinear parabolic equations with finite delay

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  • Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear parabolic equations with finite delay, where the linear principal part is positive definite with a discrete spectrum having a sufficiently large distance between some two successive point spectra, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.
    Mathematics Subject Classification: 35B40, 35B42, 49K25, 35K55, 34C30.


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