6 citations · 9 across the 13 of their papers we have counts for
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Inertial Manifolds for the 3D Cahn-Hilliard Equations with Periodic Boundary Conditions
Anna Kostianko, Sergey Zelik
The existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using the proper extension of the so-called spatial averaging…
Bifurcation to Chaos in the complex Ginzburg-Landau equation with large third-order dispersion
I. I. Ovsyannikov, D. Turaev, S. Zelik
We give an analytic proof of the existence of Shilnikov chaos in complex Ginzburg-Landau equation subject to a large third-order dispersion perturbation.
Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space
Anton Savostianov, Sergey Zelik
We prove the global well-posedness of the so-called hyperbolic relaxation of the Cahn-Hilliard-Oono equation in the whole space R^3 with the non-linearity of the sub-quintic growth…
Sharp interpolation inequalities for discrete operators and applications
Alexei Ilyin, Ari Laptev, Sergey Zelik
We consider interpolation inequalities for imbeddings of the -sequence spaces over -dimensional lattices into the spaces written as interpolation inequality be…
A note on a strongly damped wave equation with fast growing nonlinearities
Varga Kalantarov, Sergey Zelik
A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show th…
Strong Uniform Attractors for Non-Autonomous Dissipative PDEs with non translation-compact external forces
Sergey Zelik
We give a comprehensive study of strong uniform attractors of non-autonomous dissipative systems for the case where the external forces are not translation compact. We introduce se…