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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, DJB 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.

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