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Investigations of retarded PDEs of second order in time using the method of inertial manifolds with delay

Alexander V. Rezounenko — 2004

Annales de l’institut Fourier

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.

Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Rezounenko, Alexander V. — 2017

Proceedings of Equadiff 14

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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