67 citations · 251 across the 15 of their papers we have counts for
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Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
Igor Chueshov, Alexander Rezounenko
We deal with a class of parabolic nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in biology. We first prove well-p…
Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold
Tibor Krisztin, Alexander Rezounenko
Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set which is an analogous to the solution manifold used for ordi…
Dynamics of second order in time evolution equations with state-dependent delay
Igor Chueshov, Alexander Rezounenko
We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory ofnonlin…
Local properties of solutions to non-autonomous parabolic PDEs with state-dependent delays
A. V. Rezounenko
A wide class of non-autonomous nonlinear parabolic partial differential equations with delay is studied. We allow in our investigations different types of delays such as constant,…
Non-local PDEs with discrete state-dependent delays: well-posedness in a metric space
Alexander V. Rezounenko, Petr Zagalak
Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear spac…
Non-local PDEs with a state-dependent delay term presented by Stieltjes integral
Alexander Rezounenko
Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and di…