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4 papers
Non-linear partial differential equations with discrete state-dependent delays in a metric space
Alexander V. Rezounenko
We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions fro…
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…