67 citations · 251 across the 15 of their papers we have counts for
6 papers · 1 filter
Stability of a retrovirus dymanic model
Andrei Korobeinikov, Alexander Rezounenko
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we…
Viral infection model with diffusion and state-dependent delay: stability of classical solutions
Alexander Rezounenko
A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are int…
Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses
Alexander Rezounenko
A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov funct…
Partial Inertial Manifolds for infinite-dimensional dynamical systems: Example for P.D.E.s with a state-dependent delay
Alexander V. Rezounenko
We propose a new notion of Partial Inertial Manifold to study the long-time asymptotic behavior of dissipative differential equations. As shown on an example, such manifolds may ex…
On a class of PDEs with nonlinear distributed in space and time state-dependent delay term
Alexander V. Rezounenko
A new class of nonlinear partial differential equations with distributed in space and time state-dependent delay is investigated. We find appropriate assumptions on the kernel func…
Two models of partial differential equations with discrete and distributed state-dependent delays
Alexander V. Rezounenko
This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term b…