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Inertial manifolds for retarded second order in time evolution equations in admissible spaces

Cung The AnhLe Van Hieu — 2013

Annales Polonici Mathematici

Using the Lyapunov-Perron method, we prove the existence of an inertial manifold for the process associated to a class of non-autonomous semilinear hyperbolic 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 spectral points, and the Lipschitz coefficient of the nonlinear term may depend on time and belongs to some admissible function spaces.

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