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Inertial manifold with delay (IMD) for dissipative systems of second order in time is
constructed. This result is applied to the study of different asymptotic properties of
solutions. Using IMD, we construct approximate inertial manifolds containing all the
stationary solutions and give a new characterization of the K-invariant manifold.
We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...
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