# Items where Author is "Zelik, S"

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## Article

Kostianko, Anna, Titi, Edriss and Zelik, Sergey
(2018)
*Large dispersion, averaging and attractors: three 1D paradigms*
Nonlinearity, 31 (12), R317.

Ilyin, A, Patni, K and Zelik, S
(2016)
*Upper bounds for the attractor dimension of damped Navier-Stokes equations in R 2*
Discrete and Continuous Dynamical Systems - Series A, 36 (4).
pp. 2085-2102.

Kostianko, A and Zelik, S
(2016)
*Inertial Manifolds for 1D Convective Reaction-Diffusion Systems*
arXiv.

Kostianko, A, Titi, E and Zelik, S
(2016)
*Large dispersion, averaging and attractors: three 1D paradigms*
arXiv.

Chepyzhov, VV, Ilyin, AA and Zelik, SV
(2015)
*Strong trajectory and global W 1,p -attractors for the damped-driven Euler system in R 2.*
arXiv.

Bilgen, B, Kalantarov, V and Zelik, S
(2015)
*Preventing blow up by convective terms in dissipative PDEs.*
arXiv.

Kostianko, A and Zelik, S
(2015)
*Inertial manifolds for the 3D Cahn-Hilliard equations with periodic boundary conditions.*
Communications on Pure and Applied Analysis, 14 (5).
pp. 2069-2094.

Savostianov, A and Zelik, S
(2015)
*Finite Dimensionality of the attractor for the hyperbolic Cahn-Hilliard-Oono Equation in R3*
Mathematical Methods in the Applied Sciences, 39 (5).
pp. 1254-1267.

Chepyzhov, V and Zelik, S
(2015)
*Infinite Energy Solutions for Dissipative Euler Equations in R-2*
Journal of Mathematical Fluid Mechanics, 17 (3).
pp. 513-532.

Rossides, T, Lloyd, David and Zelik, S
(2015)
*Computing Interacting Multi-fronts in One Dimensional Real Ginzburg Landau Equations*
JOURNAL OF SCIENTIFIC COMPUTING, 63 (3).
pp. 799-819.

Zelik, S
(2015)
*STRONG UNIFORM ATTRACTORS FOR NON-AUTONOMOUS DISSIPATIVE PDES WITH NON TRANSLATION-COMPACT EXTERNAL FORCES*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 20 (3).
pp. 781-810.

Ilyin, A, Laptev, A and Zelik, S
(2015)
*Sharp interpolation inequalities for discrete operators and applications*
BULLETIN OF MATHEMATICAL SCIENCES, 5 (1).
pp. 19-57.

Ilyin, A, Laptev, A and Zelik, S
(2015)
*Sharp interpolation inequalities for discrete operators and applications*
BULLETIN OF MATHEMATICAL SCIENCES, 5 (1).
pp. 19-57.

Zelik, SV, Ilyin, AA and Laptev, AA
(2015)
*Sharp interpolation inequalities for discrete operators*
DOKLADY MATHEMATICS, 91 (2).
pp. 215-219.

Ilyin, A, Laptev, A, Loss, M and Zelik, S
(2015)
*One-dimensional interpolation inequalities, Carlson--Landau inequalities and magnetic Schrodinger operators*
International Mathematics Research Notices.

Kalantarov, V and Zelik, S
(2015)
*A note on a strongly damped wave equation with fast growing nonlinearities*
JOURNAL OF MATHEMATICAL PHYSICS, 56 (1), ARTN 0.

Zelik, S
(2014)
*Inertial manifolds and finite-dimensional reduction for dissipative PDEs*
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 144 (6).
pp. 1245-1327.

Bridges, Thomas, Pennant, J and Zelik, Sergey
(2014)
*Degenerate Hyperbolic Conservation Laws with Dissipation: Reduction to and Validity of a Class of Burgers-Type Equations*
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 214 (2).
pp. 671-716.

Ovsyannikov, II, Turaev, D and Zelik, S
(2014)
*Bifurcation to Chaos in the complex Ginzburg-Landau equation with large third-order dispersion*

Cherfils, L, Miranville, A and Zelik, S
(2014)
*ON A GENERALIZED CAHN-HILLIARD EQUATION WITH BIOLOGICAL APPLICATIONS*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 19 (7).
pp. 2013-2026.

Savostianov, A and Zelik, S
(2014)
*Global well-posedness and attractors for the hyperbolic Cahn-Hilliard-Oono equation in the whole space*

Turaev, DV, Warner, C and Zelik, S
(2014)
*Energy growth for a nonlinear oscillator coupled to a monochromatic wave*
REGULAR & CHAOTIC DYNAMICS, 19 (4).
pp. 513-522.

Anthony, P and Zelik, S
(2014)
*Infinite-energy solutions for the Navier-Stokes equations in a strip revisited*
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 13 (4).
pp. 1361-1393.

Mielke, A and Zelik, S
(2014)
*On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms*
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 13 (1).
pp. 67-135.

Zelik, SV and Chepyzhov, VV
(2014)
*Regular attractors of autonomous and nonautonomous dynamical systems*
DOKLADY MATHEMATICS, 89 (1).
pp. 92-97.

Savostianov, A and Zelik, S
(2014)
*Smooth attractors for the quintic wave equations with fractional damping*
ASYMPTOTIC ANALYSIS, 87 (3-4).
pp. 191-221.

Zelik, SV and Ilyin, AA
(2014)
*Green's function asymptotics and sharp interpolation inequalities*
Russian Mathematical Surveys, 69 (2).
pp. 209-260.

Savostianov, A and Zelik, S
(2013)
*Recent progress in attractors for quintic wave equations*

Kalantarov, V, Savostianov, A and Zelik, S
(2013)
*Attractors for damped quintic wave equations in bounded domains*

Zelik, S and Pennant, J
(2013)
*GLOBAL WELL-POSEDNESS IN UNIFORMLY LOCAL SPACES FOR THE CAHN-HILLIARD EQUATION IN R-3*
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 12 (1).
pp. 461-480.

Vishik, MI, Chepyzhov, VV and Zelik, SV
(2013)
*Regular attractors and nonautonomous perturbations of them*
Sbornik Mathematics, 204 (1).
pp. 1-42.

Shirikyan, A and Zelik, S
(2012)
*Exponential attractors for random dynamical systems and applications*
Stochastic Partial Differential Equations: Analysis and Computations, 1 (2).
pp. 241-281.

Eden, A, Kalantarov, VK and Zelik, SV
(2012)
*Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials*
Journal of Mathematical Physics, 54.

Turaev, D, Vladimirov, AG and Zelik, S
(2012)
*Long-Range Interaction and Synchronization of Oscillating Dissipative Solitons*
PHYSICAL REVIEW LETTERS, 108 (26), ARTN 2.

Zelik, S
(2012)
*Infinite Energy Solutions for Damped Navier-Stokes Equations in R2*
Journal of Mathematical Fluid Mechanics.

Schimperna, G, Segatti, A and Zelik, S
(2012)
*Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model*
Journal of Evolution Equations, 12 (4).
pp. 863-890.

Vishik, MI and Zelik, SV
(2011)
*Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit*
arXiv.

Efendiev, M and Zelik, S
(2011)
*Global attractor and stabilization for a coupled PDE-ODE system*
arXiv.

Eden, A, Kalanarov, V and Zelik, S
(2011)
*Counterexamples to the regularity of Mane projections and global attractors*
arXiv.

Vladimirov, AG, Turaev, D and Zelik, S
(2011)
*Synchronization of interacting temporal cavity oscillons*
Proceedings of Conference on Lasers and Electro-Optics Europe and 12th European Quantum Electronics Conference.

Kalantarov, VK and Zelik, S
(2011)
*Smooth Attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities*
arXiv.

Cherfils, L, Miranville, A and Zelik, S
(2011)
*The Cahn-Hilliard Equation with Logarithmic Potentials*
Milan Journal of Mathematics, 79 (2).
pp. 561-596.

Chepyzhov, VV, Vishik, MI and Zelik, Sergey
(2011)
*Strong trajectory attractors for dissipative Euler equations*
Journal des Mathematiques Pures et Appliquees, 96.
pp. 395-407.

Bartuccelli, MV, Deane, JHB and Zelik, S
(2010)
*Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus*
arXiv.

Vishik, MI, Zelik, SV and Chepyzhov, VV
(2010)
*Strong Trajectory Attractor for a Dissipative Reaction-Diffusion System*
DOKLADY MATHEMATICS, 82 (3).
pp. 869-873.

Schimperna, G and Zelik, S
(2010)
*Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations*
arXiv.
(Unpublished)

Miranville, A and Zelik, S
(2010)
*THE CAHN-HILLIARD EQUATION WITH SINGULAR POTENTIALS AND DYNAMIC BOUNDARY CONDITIONS*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 28 (1).
pp. 275-310.

Eden, A, Kalantarov, VK and Zelik, Sergey
(2010)
*Infinite energy solutions for the Cahn-Hilliard equation in cylindrical domains*
arXiv.

Grasselli, M, Schimperna, G and Zelik, S
(2010)
*Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term*
NONLINEARITY, 23 (3).
pp. 707-737.

Turaev, D and Zelik, S
(2010)
*Analytical Proof of Space-Time Chaos in Ginzburg-Landau Equations*
(Unpublished)

Gatti, S, Miranville, A, Pata, V and Zelik, S
(2010)
*Continuous families of exponential attractors for singularly perturbed equations with memory*
P ROY SOC EDINB A, 140.
pp. 329-366.

Segatti, A and Zelik, S
(2009)
*Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential*
NONLINEARITY, 22 (11).
pp. 2733-2760.

Efendiev, M and Zelik, S
(2009)
*Finite-dimensional attractors and exponential attractors for degenerate doubly nonlinear equations*
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 32 (13).
pp. 1638-1668.

Kalantarov, V and Zelik, S
(2009)
*Finite-dimensional attractors for the quasi-linear strongly-damped wave equation*
JOURNAL OF DIFFERENTIAL EQUATIONS, 247 (4).
pp. 1120-1155.

Turaev, D, Vladimirov, AG and Zelik, S
(2009)
*Strong enhancement of interaction of optical pulses induced by oscillatory instability*
Proceedings of European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference.

Grasselli, M, Schimperna, G, Segatti, A and Zelik, S
(2009)
*On the 3D Cahn-Hilliard equation with inertial term*
JOURNAL OF EVOLUTION EQUATIONS, 9 (2).
pp. 371-404.

Miranville, A and Zelik, S
(2009)
*Doubly nonlinear Cahn-Hilliard-Gurtin equations*
HOKKAIDO MATHEMATICAL JOURNAL, 38 (2).
pp. 315-360.

Gatti, S, Pata, V and Zelik, S
(2009)
*A Gronwall-type lemma with parameter and dissipative estimates for PDEs*
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 70 (6).
pp. 2337-2343.

Zelik, S and Mielke, A
(2009)
*Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems*
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 198 (925).
VI-95.

Grasselli, M, Miranville, A and Zelik, S
(2009)
*Preface*
Discrete and Continuous Dynamical Systems - Series S, 2 (1).

Grasselli, M, Schimperna, G and Zelik, S
(2009)
*On the 2D Cahn-Hilliard Equation with Inertial Term*
Communications in Partial Differential Equations, 34 (2), PII 909499.
pp. 137-170.

Efendiev, MA, Zelik, SV and Eberl, HJ
(2009)
*Existence and longtime behavior of a biofilm model*
Communications on Pure and Applied Analysis, 8 (2).
pp. 509-531.

Zelik, S
(2008)
*On the Lyapunov dimension of cascade systems*
COMMUN PUR APPL ANAL, 7 (4).
pp. 971-985.

Gatti, S, Miranville, A, Pata, V and Zelik, S
(2008)
*Attractors for semi-linear equations of viscoelasticity with very low dissipation*
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 38 (4).
pp. 1117-1138.

Efendiev, M and Zelik, S
(2008)
*Finite- and infinite-dimensional attractors for porous media equations*
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 96.
pp. 51-77.

Miranville, A and Zelik, S
(2008)
*Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains*
Handbook of Differential Equations: Evolutionary Equations, 4.
pp. 103-200.

Di Plinio, F, Pata, V and Zelik, S
(2008)
*On the strongly damped wave equation with memory*
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 57.
pp. 757-780.

Zelik, S
(2007)
*Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip*
GLASGOW MATHEMATICAL JOURNAL, 49.
pp. 525-588.

Miranville, A and Zelik, S
(2007)
*Finite-dimensionality of attractors for degenerate equations of elliptic-parabolic type*
NONLINEARITY, 20 (8).
pp. 1773-1797.

Mielke, A and Zelik, SV
(2007)
*Infinite-dimensional hyperbolic sets and spatio-temporal chaos in reaction diffusion systems in R-n*
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 19 (2).
pp. 333-389.

Pata, V and Zelik, S
(2007)
*A result on the existence of global attractors for semigroups of closed operators*
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 6 (2).
pp. 481-486.

Turaev, D, Vladimirov, AG and Zelik, S
(2007)
*Chaotic bound state of localized structures in the complex Ginzburg-Landau equation*
PHYSICAL REVIEW E, 75 (4), ARTN 0.

Zelik, SV
(2007)
*Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains*
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 19 (1).
pp. 1-74.

Miranville, A, Pata, V and Zelik, S
(2007)
*Exponential attractors for singularly perturbed damped wave equations: A simple construction*
ASYMPTOTIC ANALYSIS, 53 (1-2).
pp. 1-12.

Grasselli, M, Miranville, A, Pata, V and Zelik, S
(2007)
*Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials*
MATHEMATISCHE NACHRICHTEN, 280 (13-14).
pp. 1475-1509.

Pata, V and Zelik, S
(2006)
*A remark on the damped wave equation*
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 5 (3).
pp. 609-614.

Pata, V and Zelik, S
(2006)
*Global and exponential attractors for 3-D wave equations with displacement dependent damping*
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 29 (11).
pp. 1291-1306.

Pata, V and Zelik, S
(2006)
*Smooth attractors for strongly damped wave equations*
NONLINEARITY, 19 (7).
pp. 1495-1506.

Zelik, S
(2006)
*Global averaging and parametric resonances in damped semilinear wave equations*
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 136.
pp. 1053-1097.

Miranville, A and Zelik, S
(2005)
*Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions*
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 28 (6).
pp. 709-735.

Turaev, D, Zelik, S and Vladimirov, AG
(2005)
*Chaotic bound state of localized structures in the complex ginzburg-landau equation*
Optics InfoBase Conference Papers.

Efendiev, M, Zelik, S and Miranville, A
(2005)
*Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems*
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 135.
pp. 703-730.

Zelik, S
(2004)
*Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent*
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 3 (4).
pp. 921-934.

Zelik, S
(2004)
*Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 11 (2-3).
pp. 351-392.

Efendiev, MA, Fuhrmann, J and Zelik, SV
(2004)
*The long-time behaviour of the thermoconvective flow in a porous medium*
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27 (8).
pp. 907-930.

Efendiev, M, Miranville, A and Zelik, S
(2004)
*Infinite-dimensional exponential attractors for nonlinear reaction-diffusion systems in unbounded domains and their approximation*
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 460 (2044).
pp. 1107-1129.

Miranville, A and Zelik, S
(2004)
*Robust exponential attractors for Cahn-Hilliard type equations with singular potentials*
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 27 (5).
pp. 545-582.

Busca, J, Efendiev, M and Zelik, S
(2004)
*Classification of positive solutions of semilinear elliptic equations*
COMPTES RENDUS MATHEMATIQUE, 338 (1).
pp. 7-11.

Efendiev, M, Miranville, A and Zelik, S
(2004)
*Exponential attractors for a singularly perturbed Cahn-Hilliard system*
MATHEMATISCHE NACHRICHTEN, 272.
pp. 11-31.

Efendiev, M, Miranville, A and Zelik, S
(2004)
*Global and exponential attractors for nonlinear react ion-diffusion systems in unbounded domains*
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 134.
pp. 271-315.

Fabrie, P, Galusinski, C, Miranville, A and Zelik, S
(2004)
*Uniform exponential attractors for a singularly perturbed damped wave equation*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 10 (1-2).
pp. 211-238.

Efendiev, M and Zelik, S
(2003)
*The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging*
Advances in Differential Equations, 8 (6).
pp. 673-732.

Turaev, D and Zelik, S
(2003)
*Homoclinic bifurcations and dimension of attractors for damped nonlinear hyperbolic equations*
NONLINEARITY, 16 (6), PII S0951-.
pp. 2163-2198.

Zelik, SV
(2003)
*Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity*
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 56 (5).
pp. 584-637.

Efendiev, M, Miranville, A and Zelik, S
(2003)
*Infinite dimensional exponential attractors for a non-autonomous react ion-diffusion system*
MATHEMATISCHE NACHRICHTEN, 248.
pp. 72-96.

Miranville, A and Zelik, S
(2002)
*Robust exponential attractors for singularly perturbed phase-field type equations*
Electronic Journal of Differential Equations, 2002.

Efendiev, MA and Zelik, SV
(2002)
*Upper and lower bounds for the Kolmogorov entropy of the attractor for the RDE in an unbounded domain*
Journal of Dynamics and Differential Equations, 14 (2).
pp. 369-403.

Efendiev, MA, Gajewski, H and Zelik, S
(2002)
*The finite dimensional attractor for a 4th order system of cahn-hilliard type with a supercritical nonlinearity*
Advances in Differential Equations, 7 (9).
pp. 1073-1100.

Mielke, A and Zelik, SV
(2002)
*Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains*
RUSSIAN MATHEMATICAL SURVEYS, 57 (4).
pp. 753-784.

Efendiev, M and Zelik, S
(2002)
*Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homogenization*
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 19 (6).
pp. 961-989.

Zelik, SV
(2001)
*The attractor for a nonlinear hyperbolic equation in the unbounded domain*
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 7 (3).
pp. 593-641.

Efendiev, MA and Zelik, SV
(2001)
*The attractor for a nonlinear reaction-diffusion system in an unbounded domain*
Communications on Pure and Applied Mathematics, 54 (6).

Zelik, SV
(2001)
*The attractor for a nonlinear reaction-diffusion system in the unbounded domain and Kolmogorov's epsilon-entropy*
MATHEMATISCHE NACHRICHTEN, 232.
pp. 129-179.

Efendiev, M, Miranville, A and Zelik, S
(2000)
*Exponential attractors for a nonlinear reaction-diffusion system in R-3*
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 330 (8).
pp. 713-718.

Zelik, SV
(2000)
*The attractor of a quasilinear hyperbolic equation with dissipation in R-n: Dimension and epsilon-entropy*
MATHEMATICAL NOTES, 67 (1-2).
pp. 248-251.

Vishik, MI and Zelik, SV
(1999)
*Regular attractor for a non-linear elliptic system in a cylindrical domain*
SBORNIK MATHEMATICS, 190 (5-6).
pp. 803-834.

Zelik, SV
(1999)
*An attractor of a nonlinear system of reaction-diffusion equations in R-n and estimates of its epsilon-entropy*
MATHEMATICAL NOTES, 65 (5-6).
pp. 790-793.

Zelik, SV
(1998)
*A trajectory attractor of a nonlinear elliptic system in an unbounded domain*
MATHEMATICAL NOTES, 63 (1-2).
pp. 120-123.

Zelik, SV
(1997)
*Boundedness of the solutions of a nonlinear elliptic system in a cylindrical domain*
MATHEMATICAL NOTES, 61 (3-4).
pp. 365-369.

Zelik, SV
(1997)
*The Mathieu-Hill operator equation with dissipation and estimates of its instability index*
MATHEMATICAL NOTES, 61 (3-4).
pp. 451-464.

Vishik, MI and Zelik, SV
(1996)
*The trajectory attractor of a non-linear elliptic system in a cylindrical domain*
SBORNIK MATHEMATICS, 187 (11-12).
pp. 1755-1789.